Question

PLEASE HELP! Solve each of the following by using the general quadratic formula.

Answer 1

Using the quadratic formula, the solutions are:

a) $x = \frac{3 \pm \sqrt{41}}{4}$

b) $x = 1 \pm 2i$

What is a quadratic function?

A quadratic function is given according to the following rule:

$y = ax^2 + bx + c$

The solutions are:

$x_1 = \frac{-b + \sqrt{\Delta}}{2a}$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a}$

In which:

$\Delta = b^2 - 4ac$

Item a:

The coefficients are a = 2, b = -3, c = -4, hence:

• $\Delta = (-3)^2 - 4(2)(-4) = 41$

• $x_1 = \frac{3 + \sqrt{41}}{4}$

• $x_2 = \frac{3 - \sqrt{41}}{4}$

Item b:

The coefficients are a = 1, b = 2, c = 2, hence:

• $\Delta = (2)^2 - 4(1)(2) = -4$

• $x_1 = \frac{2 + \sqrt{-4}}{2} = 1 + 2i$

• $x_2 = \frac{2 - \sqrt{-4}}{2} = 1 - 2i$

More can be learned about quadratic equations at brainly.com/question/24737967

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