Question

21. If alpha and beta are the zeros of the polynomial p(x) - 3x - 12x +15, find the value of alpha square + beta square
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Answer 1

The value of $\alpha^2 + \beta^2$ = 26

Step-by-step explanation:

Given,

α and β are the zeros of the polynomial p(x) = - 3$x^2$ - 12x + 15

Here, a = - 3, b = - 12 and c = 15

To find, the value of $\alpha^2 + \beta^2$ = ?

The sum of the polynomial, α + β = $-\dfrac{b}{a}$

= $-\dfrac{-12}{-3}$

= - 4

Also,

The product of the polynomial, αβ = $\dfrac{c}{a}$

= $\dfrac{15}{-3}$

= - 5

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

⇒ $\alpha^2 + \beta^2=(-4)^2-2(- 5)=16+10=26$

∴ The value of $\alpha^2 + \beta^2$ = 26

Answer 2

answer....alpha square+ beta square is=26