If a,b,c are in geometric progression then comment on the roots of the quadratic equations axSquare+ 2bx +c=0
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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 , ax² + 2bx + c = 0 { where a ≠0}
Discriminant = (2b)² - 4 × a × c
= 4b² - 4ac
= 4b² - 4(ac)= 4b² - 4b² = 0
D = -4b² = 0 it means , both roots of quadratic equation are real and equal.
Then, common ratio must be constant.⇒ b/a = c/b
b² = ac
now, quadratic equation is given , ax² + 2bx + c = 0 { where a ≠0}
Discriminant = (2b)² - 4 × a × c
= 4b² - 4ac
= 4b² - 4(ac)= 4b² - 4b² = 0
D = -4b² = 0 it means , both roots of quadratic equation are real and equal.
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