Question

The quadratic polynomial is ax²-6x -6, whose product of zero is 4, find a

Answer 1

$Given \: Quadratic \: polynomial : ax^{2} -6x-6$

$Compare \: above \: polynomial \: with \\Ax^{2} + Bx + C, \: we \:get$

$A = a, \: B = -6 \:and \: C = -6$

$Product \: of \: zeroes = 4 \: ( given )$

$\implies \frac{C}{A} = 4$

$\implies \frac{-6}{a} = 4$

$\implies \frac{-6}{4} = a$

$\implies \frac{-3}{2} = a$

Therefore.,

$\red{ Value \: of \: a }\green { = \frac{-3}{2}}$

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Answer 2

Given that ,

The polynomial is ax² - 6x - 6 and product of zeroes is 4

We know that , the product of zeroes is given by

$\large \rm \fbox{Product \: of \: zeroes = \frac{c}{a} }$

Thus ,

$\mathsf \mapsto 4 = - \frac{ 6}{ a} \\ \\ \mathsf \mapsto a = - \frac{3}{2}$

$\therefore \sf \underline{The \: value \: of \: a \: is - \frac{3}{2}}$