Question

Find the value of 'P' for which the quadratic equation
4x²- (p - 2) x + 1 = 0 has equal roots.​

Answer 1

Answer:

- 2 or 6

Step-by-step explanation:

4x²- (p - 2) x + 1 = 0

Find the discriminant:

D = b² - 4ac

D = (p - 2)² - 4(4)(1)

D = p² - 4p + 4 - 16

D = p² - 4p - 12

D = (p + 2)(p - 6)

If the quadratic has equal roots

⇒ Discriminant = 0

Therefore:

(p + 2)(p - 6) = 0

p = - 2 or p = 6

Answer: p = - 2 or p = 6

Answer 2

Given

p(x) = 4x²- (p - 2) x + 1

Comparing with the form ax² + bx + c

a = 4

b = -(p - 2)

c = 1

For p(x) = 0

=> discriminant, D = 0

=> b² - 4ac = 0

=> [-(p - 2)]² - 4*4*1 = 0

=> p² + 4 - 4p - 16 = 0

=> p² - 4p - 12 = 0

=> p² + 2p - 6p - 12 = 0

=> p(p + 2) - 6(p + 2) = 0

=> (p - 6)(p + 2) = 0

=> p = 6 ; p = -2

Therefore P can be 6 or (-2) for which the polynomial has equal roots