Question

If a & b are the roots of x² - px + q = 0 , then a² + b² =

Answer 1

If a and b are the roots of the quadratic equation x² - px + q = 0,

Sum of roots = $a+b= -\frac{(-p)}{1}=p$

Product of roots = $ab= \frac{q}{1}=q$

we need to find the value of a²+b².

(a+b)² = a² + b² + 2ab
⇒ p² = a² + b² + 2q
⇒  a² + b² = p² - 2q

Answer 2

Here sum of the roots= -b/a
product of roots= c/a
Given b= -p
         a= 1
         c= q
sum of roots= -(-p)/1
                   = p
product of roots= q/1
                       = q
a$a{2} +b{2} = (a+b){2} + 2ab$
                        = p{2} + 2*q[/tex]