What is the sum of the squares of the roots of the equation x^2 + 2x - 143 = 0

• Quadratic Equations

What is the sum of the squares of the roots of the equation x² + 2x - 143 = 0?

1. 170
2. 180
3. 190
4. 290

Solution

Let the roots be α and β. So, sum of squares of roots = α² + β²

Sum of roots = α + β = -b/a = -2

Product of roots = αβ = c/a = -143

α² + β² = (α + β)² - 2αβ

= (-2)² - (-143) = 290

The correct option is D.