Question

If the product of the zeroes of polynomial
p(x) = ax²- 6x - 6 is 4, find the value of a and the sum of its zeroes.​

Answer 1

Step-by-step explanation:

Given:-

The product of the zeroes of polynomial

p(x) = ax^2- 6x - 6 is 4.

To find:-

Find the value of a and the sum of its zeroes.

Solution:-

Given Polynomial is p(x) = ax^2- 6x - 6

On Comparing this with the standard quadratic Polynomial ax^2+bx+c

We have

a = a

b= -6

c= -6

We know that

Sum of the zeroes = -b/a

=> -(-6)/a

Sum of the zeroes= 6/a ----------(1)

Product of the zeroes = c/a

=> -6/a

Given that

The product of the zeroes = 4

=> -6/a = 4

=>4×a = -6

=> a = -6/4

=> a = -3/2

From (1)

=Sum of the zeroes

=> 6/(-3/2)

=> 6×(-2/3)

=> 2×-2

=> -4

Sum of the zeroes = -4

Product of the zeroes= 4

a = -3/2

Answer:-

The value of a for the given problem is -3/2

The sum of the zeores = -4

Used formulae:-

• the standard quadratic Polynomial ax^2+bx+c
• Sum of the zeroes = -b/a
• Product of the zeroes = c/a