1. ## Algebraic problem q.

The roots of x^2 + px + q =0 are doublet he roots of x^2 - (b+c)x + bc =0. Write p and q in terms of b and c.
Can someone show me how to do this please?

2. For $x^2 - (b+c)x + bc =0$

Sum of roots is: $-\left(\frac{-(b+c)}{1}\right) = b+c$

Product of roots is: $\frac{bc}{1} = bc$

Clearly b and c are the roots of this equation (substitute into the equation and see). Therefore the roots of $x^2 + px + q =0$ are 2b and 2c.

Sum of roots for this equation is $-\frac{p}{1} = -p$ therefore
$-p = 2b + 2c \Rightarrow p = -2(b+c)$

Product of roots is: $\frac{q}{1} = q$ therefore

$q = 2b \times 2c = 4bc$