Question

Find the condition that zeros of polynomial p(x)= ax2 + bx + c are reciprocal to each other. with an example

Answer 1

one zero is alpha then another to be 1/alpha
$product \: of \: zeros = \frac{c}{a} \\ \alpha \times \frac{1}{ \alpha } = \frac{c}{a} \\ 1 = \frac{c}{a} \\ so \: the \: condition \: is \: a = c \\ eg \: 4{x}^{2} + 10x + 4 \\ 4 {x}^{2} + 8x + 2x + 4 \\ 4x(x + 2) + 2(x + 2) = 0 \\ (x + 2)(4x + 2) = 0 \\ x = - 2 \\ 4x = - 2 \\ x = \frac{ - 1}{2} \\ so \: we \: found \: \: that \: when \: a = c \\ zeros \: \: are \: reciprocal$

Answer 2

Hello buddy

Answer:

See the attached photo

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