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Relation between Roots and Coefficients for Quadratic

If 7 α=α2+3 a...

Question

If $7 α = α^{2} + 3$ and $β^{2} = 7 β - 3,$ then the value of $α β$ is

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Solution

$7 α = α^{2} + 3$ and $β^{2} = 7 β - 3$
$\Rightarrow α^{2} - 7 α + 3 = 0$ and $β^{2} - 7 β + 3 = 0$
Clearly, $α, β$ are the roots of $x^{2} - 7 x + 3 = 0$
$∴$ Product of roots is, $α β = \frac{c}{a} = 3$

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Relation between Roots and Coefficients for Quadratic

Standard XIII Mathematics

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