Question

(k+1) x*2-4kx+9=0
Have real and equal roots.
Find the value of k by quadratic equation

Answer 1

Given:

f(x) = (k + 1)x² - 4kx + 9 = 0

To find: value of k

Comparing it in the form ax² + bx + c = 0

we get, a = (k + 1) ; b = -4k ; c = 9

For equal roots:

Discriminant, D = 0

=> b² - 4ac = 0

=> (-4k)² - 4(k + 1) (9) = 0

=> 16k² - 36k - 36 = 0

=> 4(4k² - 9k - 9) = 0

=> 4k² - 9k - 9 = 0

=> 4k² - 12k + 3k - 9 = 0

=> 4k(k - 3) + 3(k - 3) = 0

=> (4k + 3) (k - 3) = 0

=> k = -3/4 and k = 3