Question

If the product of zeroes of the polynomial ax 2 – 6x – 6 is 4, find the value of ‘a’.​

Answer 1

If the product of zeroes of the polynomial (ax2-6x-6) is 4, find the value of a. ⇒ a=-64=-32 Ans.

Answer 2

Answer:

3/2

Step-by-step explanation:

Given:

• f(x) = ax² - 6x - 6
• Product of zeros = 4

To Find:

• The value of a.

Solution:

We know that Product of zeros = αβ = c/a

On comparing the equation with ax²+bx+c = 0

• a = a = ?
• b = 6
• c = 6

Substituting this in the equation,

• αβ = c/a

• αβ = 6/a = 4

• 6/4 = a

• a = 3/2

∴ The value of a is 3/2

To examine the nature of roots:

• b² - 4ac < 0, a ≠ 0

=> Roots are imaginary which means they are not real.

• b² - 4ac > 0, a ≠ 0

=> Roots are real but unequal.

• b² - 4ac = 0, a ≠ 0

=> Roots are real and equal.

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