Question

The sum and product of the zeroes of a quadratic polynomial p(x)=ax^2+bx+c are -3 and 2 respectively. Show that b+c =5a

Answer 1

$given \: \: \: p(x) = a {x}^{2} + bx + c \\ \\ sum = - 3 \\ \\ = > \frac{ - b}{a} = - 3 \\ \\ = > b = 3a \\ \\ product = 2 \\ \\ = > \frac{c}{a} = 2 \\ \\ = > c = 2a \\ \\ now \\ b + c = 3a + 2a \\ \\ = > b + c = 5a \\ \\ (shown)$

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