Question

The sum of the squares of the roots of the equations x²+3x+1=0 is equal to:

Answer 1

Answer:

${x}^{2} + 3x + 1 = 0 = >$

Roots of the equation are a and b

a+b => -3 and ab=>1

${(a + b)}^{2} = {( - 3)}^{2} = 9 = > {a}^{2} + {b}^{2} +$

$2ab = 9 = > {a}^{2} + {b}^{2} + 2(1) = 9 = >$

${a}^{2} + {b}^{2} + 2 = 9 = > {a}^{2} + {b}^{2} = 7 = >$

Sum of squares of roots of the equation

${x}^{2} + 3x + 1 = 0 \: is \: 7$

Hope it helps you.