Question

Write the condition to be satisfied for which equations ax² + 2bx + c = 0 and $b{x}^2-2\sqrt{ac}x+b=0$ have equal roots.

Answer 1

The given equations are

…... (1)

And, …… (2)

roots are equal.

Let be the discriminants of equation (1) and (2) respectively,

Then,

And

Both the given equation will have real roots, if

…… (3)

…... (4)

From equations (3) and (4) we get

Hence, is the condition under which the given equations have equal roots.