Question

If the difference of the roots of `2x^2-6x+c=0` is 5, what are the roots? What is the value of c?

Answer 1

`c=-8`

Explanation:

In an equation `ax^2+bx+c=9`, sum of roots is `-b/a` and product of roots is `c/a`.

Let `alpha` and `beta` be the roots of `2x^2-6x+c=0`,

then `alpha+beta=6/2=3` and `alphabeta=c/2`

Now as `(alpha+beta)^2-4alphabeta=(alpha-beta)^2`,

we have `3^2-4*c/2=5^2`

or `9-2c=25` ir `2c=9-25=-16` i.e. `c=-8`