Question

α, β are the roots of the equation $x^2$ + 14x + 10 = 0. Find the value of (${\alpha }^2$ + ${\beta }^2$).

• A. 206
• B. 196
• C. 186
• D. 176

Answer 1

The correct option is D

176

From the quadratic equation, we can find α + β = -14

αβ = 10

We know ${(\alpha +\beta )}^2$ = ${\alpha }^2$ + ${\beta }^2$ + 2αβ

${\alpha }^2$ + ${\beta }^2$ = ${(\alpha +\beta )}^2$ - 2 αβ

= ${(-14)}^2$ - 2 × 10

= 196 - 20

= 176