Find that value of k in the following quadratic equation whose roots are real and equal:
2x² + kx + 3 = 0

Question

Find that value of k in the following quadratic equation whose roots are real and equal:2x2 + kx + 3 = 0

Philoid · Accepted Answer

When we compare the above quadratic equation with the generalized one we get,

ax² + bx + c = 0

a = 2

b = k

c = 3

Since the quadratic equations have real and equal roots,

b² – 4ac = 0 for real and equal roots

⟹ (k) ² – (4 × 2 × 3) = 0

⟹ k² – 24 = 0

⟹ k² = 24

⟹ k = √( 2 × 2 × 6)

⟹ k = ± 2√6