# Math Help - [SOLVED] Quadratic equation

In what interval can $p+q$ be if we know that the sum of the squares of the roots of $x^2+px+q=0$ equals to 1 ( $x_1^2+x_2^2=1$).

2. Originally Posted by james_bond
In what interval can $p+q$ be if we know that the sum of the squares of the roots of $x^2+px+q=0$ equals to 1 ( $x_1^2+x_2^2=1$).
$\left [-1, \sqrt{2} + \frac{1}{2} \right].$

3. Originally Posted by NonCommAlg
$\left [-1, \sqrt{2} + \frac{1}{2} \right].$
Thanks but could you go into more details? Thanks in advance!

4. Originally Posted by james_bond
Thanks but could you go into more details? Thanks in advance!
there exists some $t$ such that $x_1=\cos t, \ x_2= \sin t.$ let $x=\cos t + \sin t.$ we have $p+q=-(x_1+x_2)+x_1x_2=\frac{1}{2}(x-1)^2 - 1.$ finally use the fact that $-\sqrt{2} \leq x \leq \sqrt{2}$ to finish the proof.