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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
2 5 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
aa{2} +b{2} = (a+b){2} + 2ab
                        = p{2} + 2*q[/tex]
1 5 1
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