What are the solutions of 4x2 + x = −3? Select one:

Question

asked Dec 19, 2017 106k views

2 Answers

Gerhard Brueckl · Answer 1 · 2017-12-25T06:26:06+0000

Answer:

The correct answer is c.

Explanation:

Given the equation

ax^(2)+bx+c=0

The quadratic equation solves the values of ''x'' which satisfy the original equation (In the equation I replace ± by the symbol |):

$\frac{-b|\sqrt{b^(2)-4ac}}{2a}$

The solutions of
4x^(2)+x=-3 are the same that the solutions of
4x^(2)+x+3=0

With
$a=4\\b=1\\c=3$ we replace this in the quadratic equation ⇒

$\frac{-1|\sqrt{(1)^(2)-4(4)(3)}}{(2)(4)}$ ⇒

(-1|√(1-48))/(8) ⇒

(-1|√(-47))/(8)

Given that
i^(2)=-1 (imaginary numbers property)

$\frac{-1|\sqrt{47i^(2)}}{8}=(-1|i√(47))/(8)$

The solutions are
(-1+i√(47))/(8)

and
(-1-i√(47))/(8)

The correct answer is c.