Question

The quadratic equation(m+1)x²+2(m+3)x+(m+8)=0 has equal roots.
1.The discriminant of the quadratic equation?
2.The value of m is :
3.The roots of the given equation are?​

Answer 1

Answer:

If a quadratic equation has equal roots then it's discriminant will be equal to 0

ie. b^{2} - 4 ac = 0

Here equation is ( m + 1 ) x^{2} + 2( m + 3 ) x + ( m + 8 ) = 0

Here a = ( m + 1 ) b = 2( m + 3 ) , & c = ( m + 8 )

Now substitute values in equation

D = [2 ( m + 3 )]^{2} - 4 × ( m + 1 ) ( m + 8 ) = 0

4[m^2 + 6m + 9] - [ 4 × ( m^2 + 8 + 9m ) ] = 0

4m^2 + 24m + 36 - 4m^2 - 32 - 36m = 0

-12m + 4 = 0

m = 4/12 = 1/3

Step-by-step explanation:

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