Question

if
$\alpha \: and \: \beta \: are \: the \: zeros \: of \: the \: qudrtc \: polynomil \: f{x} = ax {?}^{2} + bx + c \: then \: evalute \: \alpha {?}^{2} + \beta {?}^{2}$

Answer 1

Solution :

Given polynomial is

f (x) = ax² + bx + c ...(i)

Since, α and β are the roots of (i) no. polynomial, by the relation between roots and coefficients, we get

α + β = $-\frac{b}{a}$ ...(ii)

αβ = $\frac{c}{a}$ ...(iii)

Now, α² + β²

= (α + β)² - 2αβ

= $(-\frac{b}{a})^{2} - 2 (\frac{c}{a})$

= $\frac{b^{2}}{a^{2}}-\frac{2c}{a}$

= $\bold{\frac{b^{2} -2ca}{a^{2}}}$

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