Write the correct answer
0 of 28 Questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 28 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score |
|
Your score |
|
If \(\alpha \) and \(\beta,\gamma \) are zeroes of the polynomial \(6x^3+3x^2-5x+1 \), then find the value of \(\alpha^{-1}+\beta^{-1}+\gamma^{-1} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If the zeroes of the polynomial \(x^3-3x^2+x+1 \) are \(a-b \) and \(a+b \), find the value of \(a \) and \(b \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
sum of zeroes
On dividing \( x^3-3x^2+x+2\) by a polynomial \(g(x) \), the quotient and remainder were \(x-2 \) and \(-2x+4 \) respectively. Find \(g(x) \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Equation
If \(\alpha,\beta \) are zeroes of the polynomial \(x^2-2x-8 \), then form a quadratic polynomial whose zeroes are \( 2\alpha\) and \(2\beta \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Product
Obtain all zeroes of \(f(x)=x^4-3x^3-x^2+9x-6 \) if two of its zeroes are \((-\sqrt3) \) and \(\sqrt3 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The zeroes are
Check whether the polynomial \(g(x)=x^3-3x+1 \) is the factor of polynomial \(px(x)=x^5-4x^3-x^2+3x+1 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
No it is not a factor
If \(\alpha,\beta \) are the zeroes of the polynomial \(25p^2-15p+2 \), find a quadratic polynomial whose zeroes are \(\dfrac{1}{2\alpha} \) and \(\dfrac{1}{2\beta} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Divide \(3x^3-3x+5 \) by \(x-1-x^2 \) and verify the division algorithm
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Verify
If \(\alpha,\beta \) are the zeroes of the polynomial \(21y^2-y-1 \), find a quadratic polynomial whose zeroes are \( 2\alpha\) and \(2\beta \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find the zeroes of \(4\sqrt5x^2+17x+3\sqrt5 \) and verify the relation between the zeroes and coefficients of the polynomial.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If the polynomial \(6x^4+8x^3+17x^2+21x+7 \) is divided by another polynomial \(3x^2+4x+1 \), the remainder comes out to be \((ax+b) \), find \(a \) and \(b \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
A/Q
Find all the zeroes of the polynomial \(2x^3+x^2-6x-3 \), if two of its zeroes are \(-\sqrt3 \) and \(\sqrt3 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The zeroes are
If \(\alpha \) and \(\beta \) are the zeroes of the quadratic polynomial \(p(s)=3s^2-6s+4 \), find the value of \(\dfrac{\alpha}{\beta}+\dfrac{\beta}{\alpha}+2\left(\dfrac{1}{\alpha}+\dfrac{1}{\beta}\right)+3\alpha\beta \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(\alpha \) and \(\beta \) are the zeroes of the quadratic polynomial \(f(x)=x^2-px+q \), prove that \(\dfrac{\alpha^2}{\beta^2}+\dfrac{\beta^2}{\alpha^2}=\dfrac{p^4}{q^2}-\dfrac{4p^2}{q}+2 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(Proved)
If \(\alpha \) and \(\beta \) are the zeroes of the quadratic polynomial \(f(x)=x^2+px+q \), form a polynomial whose zeroes are \((\alpha+\beta)^2 \) and \((\alpha-\beta)^2 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If \(\alpha \) and \(\beta \) are the zeroes of the polynomial \(f(x)=x^2-2x+3 \), find a polynomial whose zeroes are \(\alpha+2 \) and \(\alpha+\beta \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Product of roots – (sum of roots)
+ Product of root
Obtain all the zeroes of the polynomial \(f(x) = 2x^4+x^3-14x-19x-6 \), if two of its zeroes are \( -2\) and \(-1 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
What must be added to \(6x^5+5x^4+11x^3-3x^2+x+5 \) so that it may be exactly divisible by \( 3x^2-2x+4\)?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
So must be added
What must be subtracted from the polynomial \(f(x)= x^4+2x^3-13x^2-12x+21 \) so that the resulting polynomial is exactly divisible by \(g(x) = x^2-4x+3 \)?
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
So must be subtracted
Find the other zeroes of the polynomial \(2x^4-3x^3-3x^2+6x-2 \), if \(-\sqrt2 \) and \( \sqrt2\) are the zeroes of the given polynomial.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
If the remainder on division of \(x^3+2x^2+kx+3 \) by \(x-3 \) is \(21 \), find the quotient and the value of \( k\). Hence, find the zeroes of the cubic polynomial \(x^3+2x^2+kx-18 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The zeroes are
If two zeroes of \( p(x) = x^4-6x^3-26x^2+138x–35 \) are \(2\pm\sqrt3 \), find the other zereos.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
other two zeroes are -5 and 7
Find other zeroes of the polynomial \( x^4+x^3-9x^2-3x+18 \), if it is given that two of its zeroes are \(\sqrt3 \) and \(-\sqrt3 \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
are zeroes.
Divide \(30x^4+11x^3-82x^2-12x+48 \) by \( (3x^2+2x-4)\) and verify the result by division algorithm.
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Verify
Find all the zeros of the polynomial \(2x^4-10x^3+5x^2+15x-12 \), if it is given that two of its zeroes are \(\sqrt{\dfrac{3}{2}} \) and \(-\sqrt{\dfrac{3}{2}} \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Find all the zeroes of the polynomial \(2x^4-3x^2-5x^2+9x-3 \), it being given that two of its zeroes are \(\sqrt3 \) and \(-\sqrt3 \)
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Zeroes of polynomial are
What must be added to the polynomial \(p(x)=5x^4+6x^3-13x^2-44x+7 \) so that the resulting polynomial is exactly divisible by the polynomial \(Q(x)=x^2+4x+3 \) and the degree of the polynomial to be added must be less than degree of the polynomial \(Q(x) \).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
So, should be added
If the polynomial \(6x^4+8x^3-5x^2+ax+b \) is exactly divisible by the polynomial \(2x^2-5 \), then find the value of \(a \) and \( b\).
Upload your answer to this question.
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.