What is the Product of the roots of the first equation?

Question

Both of the following equations have real roots.

$$ax^2 +bx+c=0$$

$$(a-b+c)x^2 -2(a-c)x+ (a+b+c)=0$$

If roots of the second equation are α and β show that $\frac{(1-α)(1-β)}{(1+α)(1+β)}$ is the product of the 2 roots of the 1st equation

Answer 1

Hint: Note that $$ \frac ca = \frac{(a-b+c)-2(a-c)+(a+b+c)}{(a-b+c)+2(a-c)+(a+b+c)}$$