If $$a$$ and $$b$$ are roots of the equation $$ax^2 + bx + c = 0$$, then which equation will have roots $$(ab + a + b)$$ and $$(ab - a - b)$$?

$$a$$ and $$b$$ are roots of the equation $$ax^2 + bx + c = 0$$

So, $$a+b=-\frac{b}{a}\ and\ \ ab=\frac{c}{a}\ .$$

So, Sum of roots of new equation is= $$\left(ab+a+b\right)+\left(ab-a-b\right)=2ab\ .$$

And, product of roots = $$\left(ab+a+b\right)\left(ab-a-b\right)=\left\{ab^2-\left(a+b\right)^2\right\}=\left(\frac{c^2}{a^2}-\frac{b^2}{a^2}\right)\ .$$

So, new equation :

$$\ x^2-\left(sum\ of\ roots\right)x+\left(product\ of\ roots\right)=0\ .$$

or, $$\ x^2-\left(\frac{2c}{a}\right)x+\left(\frac{c^2}{a^2}-\frac{b^2}{a^2}\right)=0\ .$$

or, $$\ a^2x^2-\left(2ac\right)x+\left(c^2-b^2\right)=0\ .$$

B is correct choice.