Question

If alpha and beta are the zeros of the polynomial 2x2+7x-3 find the value of alpha2+beta2

Answer 1

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Answer 2

Answer:

$\text{The value of }\alpha^2+\beta^2\text{ is }\frac{61}{4}$

Step-by-step explanation:

$\text{Given that alpha and beta are the zeros of the polynomial }2x^2+7x-3$

$\text{we have to find the value of }\alpha^2+\beta^2$

$2x^2+7x-3$

$\text{Comparing above equation with }ax^2+bx+x\text{ we get}$

$a=2, b=7, c=-3$

$\text{Sum of roots=}\alpha+\beta=\frac{-b}{a}=\frac{-7}{2}$

$\text{Product of roots=}\alpha.\beta=\frac{c}{a}=\frac{-3}{2}$

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

$=(\frac{-7}{2})^2-2(\frac{-3}{2})$

$=\frac{49}{4}+3=\frac{61}{4}$

$\text{hence, the value of }\alpha^2+\beta^2\text{ is }\frac{61}{4}$