Question

Find the value of p in quadratic equation (3+p)c2+(p+1)c+p=0 has equal roots​

Answer 1

Answer:

( - 5 ± √28 )/3

Step-by-step explanation:

For an quadratic equation to have equal roots, discriminant must be 0.

For standard equation, discriminant = b^2 - 4ac.

Here,

a = (3 + p) ; b = (p + 1), c = p

  thus,

discriminant = 0

⇒ (p + 1)² - 4(p)(p + 3) = 0

⇒ p² + 1 + 2p - 4p² - 12p = 0

⇒ - 3p² - 10p  + 1 =0

⇒ 3p² + 10p - 1 = 0

      Using quadratic formula:

⇒ p = [ -10±√10² - 4(-1)(3)]/2(3)

      = [- 10 ± √(100 + 12)]/6

      = [ - 10 ± √112 ]/6

      = [ - 10 ± 2√28]/6

      = ( - 5 ± √28 )/3