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If one root of the polynomial \(f(x) = 5{x^2} + 13x + k\) is reciprocal of the other, then the value of k is?
If the product of two zeroes of the polynomial \(f(x) = 2{x^3} + 6{x^2} – 4x + 9\) then its third zero is?
If
If a, b, g are the roots then
If \(f(x) = a{x^2} + bx + c\) has no real zeros and a+b+c < 0 then?
F(x)>0 and at x=1, f(x)<0
So, curve cuts negative gaxis
The number of real zeros of the polynomial \({x^4} + 4{x^2} + 5\)is?
Polynomial has its decrement negative.
If the polynomial \(2{x^3} + a{x^2} + 3x – 5\)and \({x^3} + {x^2} + 4x + a\) leave the same remainder when divided by x2 then the value of a is?
Factors of \({x^3} + 7{x^2} + 14x + 8\)are?
Product is equal to
When a polynomial \(2{x^3} + 5{x^2} – 2x – 6\)is divided by a polynomial x+1 then the remainder will be?
If (x+1) and (x1) are the factors of \(p{x^3} + {x^2} – 2x + q\)then the value of p and q are?
Add (1)+(2)
2q+2=0; q=1
P=2
Minimum value of the expression \({x^2} + x – 2\)is?
Minimum value
If we draw the graph of a cubic polynomial, then it will intersect the axis of x at least in?
Minimum one time as if its roots are complex they occur in pair i.e. on ereal root atleast.
Factors of \({(x + 1)^3} – {(x – 1)^3}\)are?
The value of \(({55^3} + {45^3})({55^2} – 55 \times 45 + {45^2})\)is?
If \(x + \dfrac{1}{x} = 3\)then \({x^2} + \dfrac{1}{{{x^2}}}\)is equal to?
If (x2) is a factor of \(({x^2} + 3qx – 2q)\)then the value of q is?
If \(\left( {x + \dfrac{1}{x}} \right) = 6\)then \({x^4} + \dfrac{1}{{{x^4}}}\)is?
If \({x^2} + \dfrac{1}{{{x^2}}} = 66\)then\(x – \dfrac{1}{x}\)?
If \({a^2} + {b^2} + {c^2} = 16\)and ab+bc+ca=10 then a+b+c is?
If a+b=10, ab=21 then \({a^3} + {b^3}\)is?
Factors of \({x^3} + 3{x^2} + 3x – 7\)are?
Since f(1)=0
x1 is a factor of f(x)
The value of k for which x+k is a factor of \({x^3} + k{x^2} – 2x + k + 4\)is?
F(x), g(x) are two polynomials with integer coefficient such that their HCF is 1 and LCM is \(({x^2} – 4)({x^4} – 1)\)if \(f(x) = {x^3} – 2{x^2} – x + 2\)then g(x) is?
If \({x^2} + \dfrac{1}{{{x^2}}} = 62\)then the value of \({x^4} + \dfrac{1}{{{x^4}}}\)is?
If x=2, y=1 then the value of \((4{y^2} – 9{x^2})\)\((16{y^4} + 36{x^2}{y^2} + 81{x^4})\)is?
If we divide \(3{y^4} – {y^3} + 12{y^2} + 2\)by \(3{y^2} – 1\)then remainder is?
The value of \(\left( {{a^{\dfrac{1}{8}}} + {a^{\dfrac{{ – 1}}{8}}}} \right)\left( {{a^{\dfrac{1}{8}}} – {a^{\dfrac{{ – 1}}{8}}}} \right)\left( {{a^{\dfrac{1}{4}}} + {a^{\dfrac{{ – 1}}{4}}}} \right)\left( {{a^{\dfrac{1}{2}}} + {a^{\dfrac{{ – 1}}{2}}}} \right)\)
The sum of the series \(5 + 13 + 21 + ….. + 181\)is?
If the product of the zeroes of the polynomial \(a{c^3} – 2c – 24\)is \(\dfrac{{ – 8}}{5}\). What is the value of a?
Find a cubic polynomial with the sum of its zeroes, sum of the product of its zeroes taken two at a time and the product of its zeroes are 13,52 and 60 respectively?
Let be the zeroes of the polynomial
Solving 3 equations we get
If \(\alpha \& \beta \)are the zeroes of the polynomials \({x^2} – 8x + k\)such that \({\alpha ^2} + {\beta ^2} = 34\)find the value of k.
If a and b are the zeroes of the quadratic polynomial \({x^2} – 4px – 2q\), find the value of\(\dfrac{1}{a} + \dfrac{1}{b}\)
Sum of zeroes
Product of zeroes
Find a cubic polynomial whose zeroes are \(1, – 8,\dfrac{5}{6}\)
Find zeroes of the polynomial \(30{y^2} – 13y – 56\)
Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial\({x^2} – x – 6\)?
\(\)
On solving the equation will be
Find a quadratic polynomial whose zeroes are \(\dfrac{3}{6}\& \dfrac{{ – 2}}{5}\)?
(sum of zeroes)x+product of the zero
Find a quadratic polynomial such that sum of its zeroes is 6 and difference between zeroes is 4?
What are the zeroes of the polynomial\(p(x) = 7{x^3} – 27{x^2} + 32x – 12\)?
What is the value of \(6{A^2} + {B^2} + 2AB\) where A and B are the digits of the number 39A80562B which is multiple of 72?
39A80562B will be divisible by 72,79 I.e.
let
For divisible by 8
Last digit should be 2,4,6,8 or 0
S0, 33+A+B=9K
If b is 0 then A is 3
B is 2 then A is 1
B is 4, A is 8
Find the number of integral solution for x and y if 3x+4y=17 and x>0,y>0
Let x is 1 then y is
X is 2 then y is
X is 3 then y is
X is 4 then y is
X is 5 then y is
Only x is 3 and y is 2 can be taken so, number of integral solution is 1.
If \(\dfrac{{ – 1}}{2} \le x \le \dfrac{1}{3}\& \dfrac{{ – 1}}{3} \le y \le \dfrac{1}{2}\)then what will be the smallest value of \({x^2} – {y^3}\)?
For minimum of , y should be maximum that is y is
And x should be minimum i.e., x is 0
Then
A number when divided by 1207 gives a remainder 88. What remainder should be obtained by dividing the same number by 17.
N = 1207K+88