Question

Roots of Polynomials Quick Check 1 of 51 of 5 Items Question Factor to solve the equation 4x2+12x+5=−4.(1 point) Responses x=112 1 Start Fraction 1 over 2 End Fraction x=−112 negative 1 Start Fraction 1 over 2 End Fraction x=−23 negative Start Fraction 2 over 3 End Fraction x=23 Start Fraction 2 over 3 End Fraction Skip to navigation

Answer 1

To solve the equation \( 4x^2 + 12x + 5 = -4 \), we first need to rearrange it into standard form:

\[
4x^2 + 12x + 5 + 4 = 0
\]

This simplifies to:

\[
4x^2 + 12x + 9 = 0
\]

Next, we can factor this quadratic equation. Notice that the quadratic can be factored as:

\[
(2x + 3)(2x + 3) = 0
\]

or

\[
(2x + 3)^2 = 0
\]

To find the roots, we set the factor equal to zero:

\[
2x + 3 = 0
\]

Solving for \(x\):

\[
2x = -3
\]
\[
x = -\frac{3}{2}
\]

Thus, the root of the equation is:

\[
x = -\frac{3}{2}
\]

So, the correct response from the options given should be:

**x = -1 1/2**, which is equivalent to **x = -\frac{3}{2}**.