Question

Write the condition for the roots to become equal in the equation ax2

+ bx + c = 0, (a, b, c are

real, a  0).​

Answer 1

⇒ The given quadratic equation is ax 2 +bx+c=0

⇒ Let two roots be α and β.

⇒ α=−β [ Given ]

⇒ α+β− a−b

⇒ −β+β= a−−b

⇒ 0= a −b

∴ b=0 ------- ( 1 )

We have one root negative so,

∴ αβ<0

∴ ac <0

So, here either c or a will be negative.Means, a and c will be having opposite sign. a>0,c<0 or c>0,a<0 and b=0.

Answer 2

The condition for the roots to become equal is : b²  = 4ac

Given: ax² + bx + c = 0, (a, b, c are real ).

To Find: The condition for the roots to become equal.

Solution:

• For a polynomial equation of degree 2, the discriminant ( D ) is equal to,

                      D = b² - 4ac

• For roots to be equal, the discriminant (D) must be equal to zero.

                      D = 0

                  ⇒ b² - 4ac = 0

                  ⇒ b²  = 4ac

Hence, the condition for the roots to become equal is b² = 4ac

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