Question

If α and β are the zeroes of the polynomial ax2 + bx + c, find the value of α2 + β2.

Answer 1

${ \alpha }^{2} + { \beta }^{2} = \frac{ {b}^{2} - 2ac }{ {a}^{2} }$

The polynomial is ax²+bx+c whose zeroers are:

$\alpha \: and \: \beta .$

The sum of two zeroes:

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

The product of two zeroes:

$\alpha \beta = \frac{c}{a}$

Therefore,

${ \alpha }^{2} + { \beta }^{2} = { (\alpha + \beta })^{2} - 2 \alpha \beta \\ = { (\frac{ - b}{a} })^{2} - 2 \times \frac{c}{a} \\ = \frac{ {b}^{2} }{ {a}^{2} } - \frac{2c}{a} \\ = > \frac{ {b}^{2} - 2ac }{ {a}^{2} }$

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$ItzDopeGirl❣$

Answer 2

Answer:

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