Question

If the product of the zeros of the polynomial (ax2

-6x-6) is 4 , find

the value of a.​

Answer 1

$\mathfrak{\huge{Hi !}}$

$\sf{\underline{Polynomial}}\tt{ = ax^{2} - 6x - 6}$

$\sf{\underline{Product\:of\:zeroes }}$ = 4

Let the zeroes of this polynomial be = $\tt{\alpha \:and \: \beta}$

Then : $\tt{\alpha \beta = 4}$

We know that, when a polynomial $\sf{ax^{2} + bx + c}$ has its zeroes equal to $\sf{\alpha \:and \: \beta}$ then :

$\tt{\bigstar \alpha + \beta = \frac{-b}{a}}$

$\tt{\bigstar \alpha \beta = \frac{c}{a}}$

According to this :-

$\tt{\alpha \beta = 4 = \frac{c}{a}}$

=》 c = (-6)

=》 $\tt{a = \frac{-6}{4}}$

=》 $\tt{a = \frac{-3}{2}}$