Question

Find the value of k for which the equation (k-4)x^2+2(k-4)-14=0 has equal roots

Answer 1

Answer:

k = -10

Step-by-step explanation:

Equation Given ( k - 4)x² + 2(k - 4)x - 14 = 0

on comparing this quadratic equation with general form ax² + bx + c

we get

a = ( k - 4)

b = 2( k - 4)

c = - 14

Given that the equation has equal roots, we know that roots are equal if

Discriminant which is (b² - 4ac) = 0

Putting value of a, b and c

[2(k - 4)]² - 4 ( k - 4 ) × ( -14) = 0

4 ( k - 4)²  + 56 ( k - 4) = 0

Dividing whole equation by 4( k - 4 )

( k - 4)  + 14 = 0

( k - 4 ) =  - 14

k - 4 =  - 14

k = -10