Let α and β be the roots of the equation: α+β=−p α⋅β=q But it's given that roots are p and q themselve p+q=−p p×q=q. Calculations: From (ii): p×q=q Divide both sides by q (since q≠0 ): ⇒p=1 Substitute p=1 into (i): ⇒1+q=−1⇒q=−2 Now find: p2+q2 =12+(−2)2=1+4=5
