Question

For the quadratic equation 3x^2-18x-21=0, x1 and x2 are the roots. Find:

Answer 1

Answer:

$x{_1}^2+x{_2}^2=50$

$|x_1-x_2|=8$

Step-by-step explanation:

Given equation:

$3x^2-18x-21=0$

Factor to find the roots:

$\implies 3(x^2-6x-7)=0$

$\implies x^2-6x-7=0$

$\implies x^2+x-7x-7=0$

$\implies x(x+1)-7(x+1)=0$

$\implies (x-7)(x+1)=0$

Therefore:

$\implies (x-7)=0 \implies x=7$

$\implies (x+1)=0 \implies x=-1$

Therefore, the roots of the quadratic equation are:

$x = 7,\quad x = -1$

Let  $x_1 = 7$

Let  $x_2 = -1$

$\implies x{_1}^2+x{_2}^2=7^2+(-1)^2=50$

$\implies |x_1-x_2|=|7-(-1)|=8$

Answer 2

(x_1+x_2)=-b/a=18/3=6

x_1x_2=c/a=-21/3=-7

So

• (x_1+x_2)²-2x_1x_2=x_1^2+x2²
• x1²+x2²=(6)²-2(-7)=36+14=50

(x_1-x_2)²

• x1²+x2²-2x_1x2
• 50+14
• 64

x_1-x_2=8