Question

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

• A. $176$
• B. $186$
• C. $206$
• D. $196$

Answer 1

The correct option is A

$176$

Given: $\alpha ,\beta$ are the roots of the equation $x^2+14x+10=0.$
Using the relation between roots and coefficients,
$\alpha +\beta =-14...\left(i\right)$
$\alpha \beta =10...\left(ii\right)$
We know ${(\alpha +\beta )}^2={\alpha }^2+{\beta }^2+2\alpha \beta$
${\alpha }^2$ + ${\beta }^2={(\alpha +\beta )}^2-2\alpha \beta$

$\Rightarrow {\alpha }^2$ + ${\beta }^2={(-14)}^2-2\times 10$

$=196-20$

$=176$