Question

The sum of the squares of the zeroes of the polynomial x^2 - 5x + 8 is
25
16
9
18

Answer 1

$\textbf{Given:}$

$x^2-5x+8$

$\textbf{To find:}$

$\text{Sum of the squares of the zeros}$

$\textbf{Solution:}$

$\text{Let the zeros of x^2-5x+8 be \alpha and \beta }$

$\text{Then,}$

$\alpha+\beta=\dfrac{-b}{a}$

$\alpha+\beta=\dfrac{5}{1}$

$\implies\boxed{\alpha+\beta=5}$

$\alpha\,\beta=\dfrac{c}{a}$

$\alpha\,\beta=\dfrac{8}{1}$

$\implies\boxed{\alpha\,\beta=8}$

$\text{Now,}$

${\alpha}^2+{\beta}^2$

$=(\alpha+\beta)^2-2\,\alpha\beta$

$=(5)^2-2(8)$

$=25-16$

$=9$

$\implies\boxed{{\alpha}^2+{\beta}^2=9}$

$\therefore\textbf{Sum of the squares of zeros of x^2-5x+8 is 9}$

Find more:

The equation whose roots are smaller by 1 than those of 2x2 – 5x + 6 = 0 is 

a) 2x^2– 9x + 13 = 0

b) 2x^2– x + 3 = 0 

c) 2x^2+ 9x + 13 = 0

d) 2x^2 + x + 3 = 0​

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If alpha,beta are the roots of equation x^2-5x+6=0 and alpha > beta then the equation with the roots (alpha+beta)and (alpha-beta) is

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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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