# If the roots of ax^2 + bx +c = 0 are in the ratio 3:4, prove that 12b^2 = 49ac?

##### 2 Answers

#### Explanation:

Reminder of the improved quadratic formula (Socratic Search)

Determinant -->

The 2 real roots are:

The ration

Cross multiply -->

- 3b - 3d = 4d - 4b

4b - 3b = 4d + 3d

b = 7d.

Square both sides -->

Let

Hence

Again it is also given that

Let

So

Hence

Proved