Correct Answer - Option 4 : 290
Concept:
Let us consider the standard form of a quadratic equation, ax2 + bx + c = 0
Let α and β be the two roots of the above quadratic equation.
- The sum of the roots of a quadratic equation given by: \({\rm{\alpha }} + {\rm{\beta }} = - \frac{{\rm{b}}}{{\rm{a}}} = - \frac{{{\rm{coefficient\;of\;x}}}}{{{\rm{coefficient\;of\;}}{{\rm{x}}^2}}}\)
- The product of the roots is given by: \({\rm{\alpha \beta }} = \frac{{\rm{c}}}{{\rm{a}}} = \frac{{{\rm{constant\;term}}}}{{{\rm{coefficient\;of\;}}{{\rm{x}}^2}}}\)
Calculation:
Given equation is x2 + 2x - 143 = 0
To Find: Sum of the squares of the roots
Let α and β be the two roots of the above quadratic equation.
Now, Sum of roots = α + β = -2
Product of roots = αβ = -143
(α + β)2 = α2 + β2 + 2αβ
⇒ (-2)2 = α2 + β2 + 2 × (-143)
⇒ 4 = α2 + β2 - 286
∴ Sum of the squares of the roots = α2 + β2 = 290