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.