Question

If α and β are the roots of the equation x² - px + q = 0, then \(\sum {{(\alpha ^2 + \beta^2)}} \) is
1. p² + 2q
2. p + 2q
3. p² - 2q
4. p - 2q

Answer 1

Correct Answer - Option 3 : p² - 2q

Concept:

For standard quadratic equation:

ax² + bx + c = 0

Sum of root \(= \frac{{ - b}}{a}\)

Product of roots \(= \frac{c}{a}\)

Analysis:

equation x² – px + q = 0

Since roots are α and β

\(\alpha + \beta = \frac{{ - \left( p \right)}}{1} = p\)

α β = q

α² + β² = (α + β)² – 2 α β

α² + β² = p² – 2q