Question

If one of the roots of an equation, x^2-2x+c = 0 is thrice the other, then c=?

Answer 1

Let the roots be αα and 33αα.

We are given the equation:

3x2−4x+k=03x2−4x+k=0

We know that for a equation ax2+bx+c=0ax2+bx+c=0,

Sum of the roots = −ba−ba

and

Product of the roots = caca.

So, we have:

α+3α=4α=43α+3α=4α=43

⇒α=13⇒α=13.

and

α×3α=3α2=3(13)2=13=k3α×3α=3α2=3(13)2=13=k3.

So, k=1k=1!