Question

Find the value of `c` for which the roots of `2x^2-21x+c=0` are in the ratio `1:2`?

Answer 1

`c=49`

Explanation:

When we have two roots of `ax^2+bx+c=0`, then

sum of roots is `-b/a` and product of roots ic `c/a`.

As roots of `2x^2-21x+c=0` are in the ratio `1:2`, let the roots be `alpha` and `2alpha`.

Then `alpha+2alpha=21/2` i.e. `3alpha=21/2` or `alpha=7/2`.

and hence as `c/2` is product of roots, we have

`c/2=7/2xx2xx7/2=49/2`

or `c=49`