Question

if a, band c are in geometric progression then comment on the roots of the quadratic equation
$2x { }^{2} + 2bx + c = 0(a not equal to 0)$

Answer 1

a , b and c are in geometric progression.
Then, common ratio must be constant.⇒ b/a = c/b
b² = ac

now, quadratic equation is given , 2ax² + 2bx + c = 0 { where a ≠0}
Discriminant = (2b)² - 4 × 2a × c
= 4b² - 8ac
= 4b² - 8(ac)= 4b² - 8b² = - 4b²
D = -4b² < 0 it means quadratic equation has no real roots