Question

If a, b, c are real numbers in A.P, then the roots of ax^2 + bx + c = 0 are real for ....​

Answer 1

Since a,b,c are in A.P.

b = (a + c)/2 ( eq 1)

We r given with the quadratic equation

ax^2 + bx + c = 0

Determinant =

b^2 - 4ac

((a + c)/2)^2) - 4ac ( b = (a+c)/2)

(a^2 + c^2 + 2ac -16ac)/4

(a^2 + c^2 - 2ac - 12ac)/4

((a - c)^2)/4 - 3ac

Roots will be real only for the equation if 3ac is smaller than ((a-c)^2)/4

Hope this would help :)