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If the product of zeroes of the polynomial $a x 2 − 6 x − 6$ is $6$ , find the value of $a$ .

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− 1

2

− 3

4

answer is A.

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Detailed Solution

Given that for the polynomial

a x 2 − 6 x − 6

, the product of the zeroes is

6

. We need to find the value of

a

.
When

α

and

β

are the zeroes of quadratic polynomial, the two equations formed with zeroes are given as:

α + β = − b a

and

α β = c a

where

b

is the coefficient of linear term,

c

is constant while

a

is the coefficient of quadratic term in quadratic polynomial.
Hence, from the polynomial

a x 2 − 6 x − 6

we have,

α + β = − (− 6) a ⇒ α + β = 6 a

and

α β = − 6 a

Since it is given that product of zeroes for the given polynomial is 6, therefore, we have,

− 6 a = 6 ⇒ a = − 6 6 ⇒ a = − 1

Hence for the given polynomial

a x 2 − 6 x − 6

, the value of

a

− 1

respectively.
Therefore, option 1 is correct.

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