Question

If and are the roots of equation x2 2x + 4 = 0, then what is the equation whose roots are 3/2 and 3/2?

Answer 1

Just expand (x - (3/2))(x - (3/2)). That's all!

Well, the quadratic equation ax² + bx + c = 0 has roots α & β if and only if ax² + bx + c = (x - α)(x - β).

So the equation is,

(x - (3/2))(x - (3/2)) = x² - 3x + 9/4 = 0

Suitable integers can be used to multiply with it to make coefficients integers.

Here 4 is multiplied, so we get 4x² - 12x + 9 = 0.