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Quadratic Formula

If α ,β are...

Question

If $α, β$ are the zeros of the polynomial $p (x) = 2 x^{2} - 7 x + 3$ , then find the value of $α^{2} + β^{2}$ .

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Solution

$2 x^{2} - 7 x + 3 = P (x)$
$2 x^{2} - 7 x + 3 = 0$ Roots are $α, β$
$α + β = \frac{7}{2}$
$α β = \frac{3}{2}$
$α^{2} + β^{2} = {(α + β)}^{2} - 2 α β = {(\frac{7}{2})}^{2} - 2 (\frac{3}{2}) = \frac{49}{4} - 3 = \frac{37}{4}$

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