Question

If the quadratic equation ax² +bx + c = 0 has equal roots then find c in terms of a and b.

Answer 1

For a quadratic equation ax² + bx + c =0, the term b² - 4ac is called discriminant (D) of the quadratic equation because it  determines  whether the quadratic equation has real roots or not ( nature of roots).
D=  b² - 4ac
So a quadratic equation ax² + bx + c =0, has

Two equal real roots, if b² - 4ac = 0 , then x= -b/2a or -b/2a

SOLUTION:

GIVEN:ax² + bx + c =0,
D=  b² - 4ac
0 = b² - 4ac  [ D= 0 , equal roots] given
b² - 4ac= 0
b² = 4ac

c = b² / 4a

Hence, the value of c in terms of a & b = c = b² / 4a.

HOPE THIS WILL HELP YOU...

Answer 2

Given quadratic equation is:

ax² + bx + c = 0

We know that, when a given equation have equal roots then its discriminant is always equal to be zero.

⇒ D = 0

⇒ b² - 4ac = 0

⇒ - 4ac = -b²

⇒ 4ac = b²

⇒ c = b²/4a


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