Find value of k, for which equation x2 + 5kx + 16 = 0 has no real roo

1.	Find value of k, for which equation x2 + 5kx + 16 = 0 has no real roots.
Answer» Given equation x² + 5kx + 16 = 0 Comparing it by general quadratic equation ax² + bx + c = 0 a = 1, b = 5k, c = 16 Discriminant (D) = b² – 4ac = (5k)² – 4 × 1 × 16 = 25k² – 64 If Discriminant (D) < 0, then roots will not be real. i.e. D < 0 ⇒ 25k² – 64 < 0 ⇒ (5k – 8)(5k + 8) < 0 ⇒ 5k – 8 < 0 or 5k + 8 < 0 ⇒ k < 8/5 or k > -8/5 Hence, value of k will be smaller than 8/5 or greater than -8/5

Find value of k, for which equation x2 + 5kx + 16 = 0 has no real roots.

Answer»

Given equation x² + 5kx + 16 = 0

Comparing it by general quadratic equation ax² + bx + c = 0

a = 1, b = 5k, c = 16

Discriminant (D) = b² – 4ac

= (5k)² – 4 × 1 × 16

= 25k² – 64

If Discriminant (D) < 0, then roots will not be real.

i.e. D < 0

⇒ 25k² – 64 < 0

⇒ (5k – 8)(5k + 8) < 0

⇒ 5k – 8 < 0 or 5k + 8 < 0

⇒ k < 8/5 or k > -8/5

Hence, value of k will be smaller than 8/5 or greater than -8/5