Question

Find the value of ‘k’ for which the following quadratic equation has real roots:

2x² + kx − 4 = 0

Answer 1

Given:

2x² + kx − 4 = 0

For a quadratic equation ax² + bx + c = 0, the discriminant is:

D = b² − 4ac

For the equation to have real roots, the discriminant must be: 

D ≥ 0

Identify coefficients

From the equation:

a = 2

b = k

c = −4

D = k² − 4(2) (−4)

= k² + 32

Apply the condition for real roots

This is always true for all real values of k, since:

k² ≥ 0 for all real numbers

And k² + 32 > 0 for all real k

The equation has real roots for all real values of k​.