Question

If α and β are the zeroes of the polynomial
xsquare+ x – 1, the evaluate α + β + αβ.

Answer 1

$\textbf{Given:}$

$\text{ \alpha and \beta are zeros of x^2+x-1 }$

$\textbf{To find:}$

$\text{The value of \alpha+\beta+\alpha\beta }$

$\textbf{Solution:}$

$\text{Since \alpha and \beta are zeros of x^2+x-1 , we have}$

$\text{Sum of the zeros}=\dfrac{-b}{a}$

$\alpha+\beta=\dfrac{-1}{1}$

$\implies\alpha+\beta=-1$

$\text{Product of the zeros}=\dfrac{c}{a}$

$\alpha\,\beta=\dfrac{1}{1}$

$\implies\alpha\,\beta=1$

$\text{Now,}$

$\alpha+\beta+\alpha\,\beta$

$=-1+1$

$=0$

$\therefore\textbf{The value of \bf\alpha+\beta+\alpha\beta is 0}$

$\textbf{Find more:}$

1)If alpha and beta are zeroes of quadratic polynomial x2 -(k+6x)+2(2k-1) 

find k if alpha +beta=1/2alpha beta 

2)If alpha and beta are zeroes of x2-6x+a, find the value of a if 3alpha+2beta=20

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