Question

(JUC TUUL
so
2) Determine k
that the equation
x2-3kx + 64 = 0 has no real roots.​

Answer 1

Step-by-step explanation:

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

Hope it helps