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If \(\alpha \ \& \ \beta \) are the zeroes of \(f(x) = {x^2} + x + 1\) then \(\dfrac{1}{\alpha } + \dfrac{1}{\beta }\) is?
If one zero of two polynomial \(f(x) = ({k^2} + 4){x^2} + 13x + 4k\) is reciprocal of the other, then k is?
Let first zero is
Second zero
If sum of the zeroes of the polynomial \(f(x) = 2{x^3} – 3k{x^2} + 4x – 5\)is 6 then the value of k is?
Sum of zeroes
If \(\alpha ,\beta \) are the zeroes of the polynomial \(p(x) = {x^2} – p(x + 1) – c\) then \((\alpha + 1)(\beta + 1)\) is?
If the polynomial \(f(x) = a{x^3} + bx – c\) is divisible by \(g(x) = {x^2} + bx + c\) then ab is?
*** QuickLaTeX cannot compile formula: {x^2} + bx + c\mathop{\left){\vphantom{1\begin{array}{l}a{x^3} + bx  c\\\underline \begin{array}{l}a{x^3} + ab{x^2} + acx\\  \,\,\,\,\,\,  \,\,\,\,\,\,\,\,\,\,\,\,\,  \end{array} \\  ab{x^2} + \left( {b  ac} \right)x  c\\\underline \begin{array}{l}  ab{x^2}  a{b^2}x  abc\\ + \,\,\,\,\,\,\,\, + \,\,\,\,\,\,\,\,\,\,\,\,\,\, + \end{array} \\\left( {b  ac + a{b^2}} \right)x + abc  c\end{array}}}\right) \!\!\!\!\overline{\,\,\,\vphantom 1{\begin{array}{l}a{x^3} + bx  c\\\underline \begin{array}{l}a{x^3} + ab{x^2} + acx\\  \,\,\,\,\,\,  \,\,\,\,\,\,\,\,\,\,\,\,\,  \end{array} \\  ab{x^2} + \left( {b  ac} \right)x  c\\\underline \begin{array}{l}  ab{x^2}  a{b^2}x  abc\\ + \,\,\,\,\,\,\,\, + \,\,\,\,\,\,\,\,\,\,\,\,\,\, + \end{array} \\\left( {b  ac + a{b^2}} \right)x + abc  c\end{array}}}} \limits^{\displaystyle\,\,\, {ax  ab}} *** Error message: Argument of \begin has an extra }. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}} Paragraph ended before \begin was complete. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}} Missing } inserted. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}} Extra }, or forgotten $. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}} Missing } inserted. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}} Extra }, or forgotten $. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}} Missing } inserted. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}} Extra }, or forgotten $. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}} Missing } inserted. leading text: ...c + a{b^2}} \right)x + abc  c\end{array}}
The remainder must be zero
Then
If one root of the polynomial \(f(x) = 5{x^2} + 13x + k\) is reciprocal of the other, then value of k is?
Find the value of the polynomial \(p(x) = {x^2} + 3x – 2\) when x=1.
If two of the zeroes of the cubic polynomial \(a{x^3} + b{x^2} + cx + d\) are each equal to zero, then the third zero is.
Let be its zeroes
If two zeroes of \({x^3} + {x^2} – 5x – 5\) are \(\sqrt 5 \ \& – \ \sqrt 5 \) then its third zero is?
The product of the two zeroes \({x^3} + 4{x^2} + x – 6\) is?
a=1,b=4,c=1,d=6
What should be subtracted to the polynomial \({x^2} – 16x + 30\) so, that 15 is the zero of the resulting polynomial?
F(15)=0
A quadratic polynomial, the sum of whose zeroes is 0 and is zeroes is 3 is?
If one zero of the quadratic polynomial \({x^2} + 3x + k = 2\) then the value of k is?
The value of p for which the polynomial \({x^3} + 4{x^2} – px + 8\) is exactly divisible by (x2) is?
If \(\alpha ,\beta \) are zeroes of \({x^2} – 6x + k\) what is the value of k if \( 3\alpha + 2\beta = 20\)
What are the zeroes of the polynomial \(p(x) = 7{x^3} – 27{x^2} + 32x – 12\)
If (x+1) is a factor of \({x^2} – 3ax + 3a – 7\)then find the value of a?
If \(\alpha \ \&Â \ \beta \) are zeroes of \({x^2} – 4x + 1\) then \(\dfrac{1}{\alpha } + \dfrac{1}{\beta } – \alpha \beta \) is?
Identify the quadratic polynomial with no zeroes?
The curve of a quadratic polynomial with no zeroes doesnâ€™t intersect the xaxis at any point.
If \(f(x) = a{x^2} + bx + c \) has no real zeroes and \( a + b + c < 0\) then
But
Find the common zeroes of the polynomial \({x^3} + 5{x^2} – 9x – 45\) and \({x^3} + 8{x^2} + 15x\)
The sum of the zeroes of the polynomial \({x^2} – 6x + 5\) is?
Sum
The product of the zeroes of the polynomial \(4{x^2} – 7x\) is?
product
The polynomial whose zeroes are 5, 6 are?
Sum of zeroes =5+6=11
Product
(sum of roots)x + product of zeroes
The polynomial whose zeroes are \(3 + \sqrt 3 , \ 3 – \sqrt 3 \) is?
Sum of zeroes
Polynomial
If \(\alpha \ \& \ \beta \)are the roots of the polynomial \(a{x^2} + bx + c\), the value of \({\alpha ^2} + {\beta ^2}\) is?
Sum of zeroes
Product of zeroes
If a and b are the zeroes of polynomial \(3{x^2} + 11x – 4\), the value of \(\dfrac{a}{b} + \dfrac{b}{a}\) is?
If p and q are the zeroes of the polynomial \(p(x) = {x^2} – 5x + k\) such that pq=1, the value of k is?
From 1 and 3
P=3 and q=2
Substituting in equation 2 we get
K=6
If l and m are zeroes of the polynomial \(p(x) = 2{x^2} – 5x + 7\) find a polynomial whose zeroes are 2l+3 and 2m+3
If one of the zeroes of the quadratic polynomial \((p – 1){x^2} + px + 1\) is 3, then the value of p is?