Question

If the product of zeros of the polynomial ax² - 6x - 6 is 4 ,find the value of a.​

Answer 1

Answer:

$\sf{The \ value \ of \ a \ is \ \dfrac{-3}{2}.}$

Given:

• The given quadratic polynomial is ax²-6x-6.

• The product of the zeroes is 4.

To find:

• The value of a.

Solution:

$\sf{The \ given \ quadratic \ polynomial \ is}$

$\sf{ax^{2}-6x-6}$

$\sf{Here, \ a=a, \ b=-6 \ and \ c=-6}$

$\sf{We \ know, \ Product \ of \ zeroes=\dfrac{c}{a}}$

$\sf{\therefore{\dfrac{-6}{a}=4}}$

$\sf{\therefore{a=\dfrac{-6}{4}}}$

$\sf{\therefore{a=\dfrac{-3}{2}}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ a \ is \ \dfrac{-3}{2}.}}}$

Answer 2

Given ,

• The product of zeros of the polynomial ax² - 6x - 6 is 4

We know that , the product of zeroes of polynomial is given by

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

Thus ,

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

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