Question

Find the values of k for which the given equation has equal roots.
x2 + k(4x + k -1) + 2 = 0

Answer 1

Values of k for which the given equation has equal roots are 2/3 or - 1.

Step-by-step explanation:

Given Equation :

x² + k( 4x + k - 1 ) + 2 = 0

=> x² + 4kx + k² - k + 2 = 0

Comparing the above quadratic equation with ax² + bx + c = 0 we get,

• a = 1
• b = 4k
• c = k² - k + 2

For a quadratic equation to have equal Discriminat b² - 4ac = 0

=> b² - 4ac = 0

=> (4k)² - 4(1)( k² - k + 2 ) = 0

=> 16k² - 4k² + 4k - 8 = 0

=> 12k² + 4k - 8 = 0

=> 3k² + k - 2 = 0

=> 3k² + 3k - 2k - 2 = 0

=> 3k(k + 1) - 2(k + 1) = 0

=> (3k - 2)(k + 1) = 0

=> 3k - 2 = 0 or k + 1 = 0

=> k = 2/3 or k = - 1

Therefore the values of k for which the equation has equal roots are 2/3 and - 1.