Question

What is the positive value of k for which the
equations x2 + kx +144=0 and x2 -12 x + k
will have real roots?​

Answer 1

Answer:

Given:

x² + kx + 144 = 0 & x² - 12x + k = 0

Have real roots.

To find:

The value of k (positive value)

Solution:

» x² + kx + 144 = 0

Here, a = 1, b = k and c = 144

For real roots, k² - 576 ≥ 0

Therefore, k ≥ 24 ... (1)

» x² - 12x + k = 0

Here, a = 1, b = -12 & c = k

For real roots, 144 - 4k ≥ 0

» 4k ≤ 144

» k ≤ 36 ... (2)

From (1) and (2)

» k € [24, 36]