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Zeroes of a Polynomial

Find the sum ...

Question

Find the sum and product of zeroes of polynomial $a x^{2} - 5 x + c$ is equal to 10,find a & c.

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Solution

We have,

$P (x) = x^{2} - (s u m o f r o o t s) x + (p r o d u c t o f r o o t s)$

$x^{2} - (10) x + 10 = 0$

$\frac{1}{2} x^{2} - 5 x + 5 = 0$ ........(1)

Given, $a x^{2} - 5 x + c = 0$ .......(2)

comparing (1) and (2), we get,

$\Rightarrow a = \frac{1}{2}, c = 5$

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