Question

The quadratic formula gives which roots for the equation 2x^2+7x+-2

Answer 1

The quadratic expression is given $2x^{2} +7x-2$ where the constants are

$a=2$
$b=7$
$c=-2$

Quadratic formula to find the roots is given as

x₁,₂ = [-b plus minus √(b)²-4ac)] ÷ 2a

Substitute a, b, and c from our expression we have

x₁,₂ = [-7 plus minus √(7)²-(4×2×-2)] ÷ 2(2)
x₁,₂ = [-7 plus minus√65] ÷ 4

from here we'll work out x₁ and x₂ separately

x₁ = (-7+√65) ÷ 4 = 0.266 (round to 3 dp)
x₂ = (-7-√65) ÷ 4 = -3.766 (round to 3 dp)