Question

Q6
. If a and B are the zeroes of the polynomial x² - 6x + k, find the value of k, such that a²+b²= 40.​

Answer 1

Answer:

Given :

• A and B are the zeroes of the polynomial x² - 6x + k.
• A² + B² = 40.​

To Find :

• The value of k.

Solution :

x² - 6x + k

a = 1 , b = -6 , c = k

We know that :

Sum of the zeroes = -b/a

⇒ A + B = -(-6)/1

⇒ A + B = 6

Product of the zeroes = c/a

⇒ AB = k/1

⇒ AB = k

Using Formula : A² + B² = (A + B)² - 2AB

⇒ 40 = 6² - 2k

⇒ 40 = 36 - 2k

⇒ 2k = 36 - 40

⇒ 2k = -4

⇒ k = -4/2

⇒ k = -2

• Hence, the value of k = -2