Question

Find the value of K if the quadratic equation x²+3kx+k+7=0 has equal roots

Answer 1

discriminant = 0

9 k.k- 4(k+7) = 0

9 k.k - 4 k-28 = 0

k= 4+-√16+1008)/18
=4+-32/18
= 36/18 ,-30/18
= 2,-5/3

Answer 2

Quadratic equation : x^2 + 3kx + k + 7 = 0

                              ⇒  x^2 + 3kx + ( k + 7 ) = 0

On comparing the given equation with ax^2 + bx + c = 0, we get the following information :

a = 1   ,  b = 3k    ,   c = k + 7

Discriminant is b^2 - 4ac , but for equal & real roots discriminant is 0.

b^2 - 4ac = 0

( 3k )^2 - 4{ 1 × ( k + 7 ) } = 0

9k^2 - 4{ k + 7 } = 0

9k^2 - 4k - 28 = 0

9k^2 - ( 18 - 14 ) k - 28 = 0

9k^2 - 18k + 14k - 28 =  0

9k( k - 2 ) + 14( k - 2 ) = 0

( k - 2 ) ( 9k + 14 ) = 0

                          By Zero Product Rule

k = 2 or k = - 14 / 9

Therefore, value of k is 2 or - 14 / 9

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