Question

14. If 2 is a root of the equation x2 + kx + 12 = 0 and the equation x² + kx + p = 0
Has equal roots, find the value of p.​

Answer 1

Answer:-

Given:-

• 2 is a root of the equation x² + kx + 12 = 0 and the equation x² + kx + p = 0 has equal roots

To find:-

• The value of p

Solution:-

x² + kx + 12 = 0

root of the above equation is 2

2² + k(2) + 12 = 0

4 + 2k + 12 = 0

2k = -12 - 4

2k = -16

k = -16/2

k = -8

Here, the value of k = -8

Then,

x² + kx + p = 0

x² -8x + p = 0

We have to find value of p

Condition for equal roots is "b² = 4ac"

∴(-8)² = 4(1)(p)

⇒64 = 4p

⇒p = 64/4

⇒p = 16

Therefore, the value of p is "16"