If a and b are the roots of x2 – px + q = 0, then a2 + b2 =………

1.	If a and b are the roots of x2 – px + q = 0, then a2 + b2 =………………… A) p2 + 2q B) p2 – q2C) p2 – 2q D) p2 + q2
Answer» Correct option is (C) p² – 2q Given that a and b are roots of equation \(x^2-px + q = 0\) \(\therefore\) Sum of roots \(=\frac{-(-p)}1=p\) \(\Rightarrow\) a+b = p _____________(1) And product of roots \(=\frac q1=q\) \(\Rightarrow\) ab = q _____________(2) Now, \(a^2+b^2=(a+b)^2-2ab\) = \(p^2-2q\) Correct option is C) p² – 2q

If a and b are the roots of x2 – px + q = 0, then a2 + b2 =………………… A) p2 + 2q B) p2 – q2C) p2 – 2q D) p2 + q2

Answer»

Correct option is (C) p² – 2q

Given that a and b are roots of equation

\(x^2-px + q = 0\)

\(\therefore\) Sum of roots \(=\frac{-(-p)}1=p\)

\(\Rightarrow\) a+b = p _____________(1)

And product of roots \(=\frac q1=q\)

\(\Rightarrow\) ab = q _____________(2)

Now, \(a^2+b^2=(a+b)^2-2ab\)

= \(p^2-2q\)

Correct option is C) p² – 2q