If the zeroes of the polynomial ${a x}^{2} + b x + c$ are in the ratio $4 : 5$ find $a : b : c$

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Solution

The zeros of polynomial are $4 x, 5 x$

Sum of zeros is $\frac{b}{a} = 4 x + 5 x = 9 x$

Product of zeros is $\frac{c}{a} = 4 x (5 x) = 20 x^{2}$

$⟹ a = x, b = 9 x, c = 20 x$

$\Rightarrow$ $a : b : c = 1 : 9 : 20$

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