Question

f(x) = x^2 + 4x + 20 find the real roots. take your time if you want :)

Answer 1

Answer:

No real roots

$x = -2 + 4i, x = -2 - 4i$

Step-by-step explanation:

Hello!

We can solve the quadratic by using the Quadratic Formula.

Standard form of a Quadratic: $ax^2 + bx + c = 0$

Quadratic Equation: $x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$

Given our Equation: $f(x) = x^2 + 4x + 20$

• a = 1
• b = 4
• c = 20

Set the equation to 0 and solve using the formula.

Solve

• $x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$
• $x = \frac{-4\pm\sqrt{4^2 - 4(1)(20)}}{2(1)}$
• $x = \frac{-4\pm\sqrt{16 - 80}}{2}$
• $x = \frac{-4\pm\sqrt{-64}}{2}$
• $x = \frac{-4\pm8i}{2}$
• $x = -2 + 4i, x = -2 - 4i$

There are no real roots to the quadratic.