Question

If the roots of ax²+2bx+c=0, a≠0, a, b, c ∈ R are real and equal, then prove that a:b=b:c.

Answer 1

Hi ,

It's given that ,

ax² + 2bx + c = 0

Discriminant = 0

( 2b )² - 4ac = 0

[ Since roots are equal ]

4b² - 4ac = 0

4b² = 4ac

b² = ac

b × b = ac

b/c = a/b

b : c = a : b

I hope this helps you.

: )