Question 13

If the difference between the roots of the equation $$Ax^2 - Bx + C = 0$$ is 4, then which of the following is TRUE?

Solution

Let say , x and y are two roots .

So,

$$x+y=-\frac{-B}{A}=\frac{B}{A}\ and\ \ xy=\frac{C}{A}\ .$$

So, $$x-y=4\ .$$

or, $$\left(x-y\right)^2=4^2\ .$$

or, $$\left(x+y\right)^2-4xy=16\ .$$

or, $$\frac{B^2}{A^2}-\frac{4C}{A}=16\ .$$

or, $$B^2-4AC=16A^2\ .$$

or, $$B^2-10A^2=4AC+6A^2\ .$$

B is correct choice.

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