MathematicsIf the product of zeroes of the polynomial ax2-6x-6 is 4, find the value of a.

If the product of zeroes of the polynomial $a x^{2} - 6 x - 6$ is 4, find the value of a.

Given polynomial,

a x^{2} - 6 x - 6

. The product of zeroes of the given polynomial is 40.
Let α, β be the zeroes of given polynomial then,

αβ = 4

… (1)
We know that, in any equation

a x^{2} + bx + c = 0

Sum of zeroes = \frac{- b}{a}

and

Product of zeroes = \frac{c}{a}

Then,

α \times β = \frac{- 6}{a}

\Rightarrow 4 = \frac{- 6}{a}

{using equation (1)}

\Rightarrow a = \frac{- 6}{4}

\Rightarrow a = \frac{- 3}{2}

Hence, option (1) is correct.

JEE