How do you use the quadratic formula to solve 4x^2+16x+15=0?

1 Answer
Nov 9, 2016

See explanation...

Explanation:

4x^2+16x+15 = 0

is in the form:

ax^2+bx+c = 0

with a=4, b=16 and c=15

The roots are given by the quadratic formula:

x = (-b+-sqrt(b^2-4ac))/(2a)

color(white)(x) = (-16+-sqrt(16^2-4(4)(15)))/(2*4)

color(white)(x) = (-16+-sqrt(256-240))/8

color(white)(x) = (-16+-sqrt(16))/8

color(white)(x) = (-16+-4)/8

color(white)(x) = (-4+-1)/2

That is:

x = -5/2 or x = -3/2

color(white)()
Footnote

In this particular example, I would probably have favoured an AC method rather than the quadratic formula.

Given:

4x^2+16x+15 = 0

Find a pair of factors of AC=4*15=60 with sum B=16

The pair 10, 6 works.

Use this pair to split the middle term and factor by grouping:

0 = 4x^2+16x+15

color(white)(0) = (4x^2+10x)+(6x+15)

color(white)(0) = 2x(2x+5)+3(2x+5)

color(white)(0) = (2x+3)(2x+5)

Hence roots x = -3/2 and x = -5/2

Note that the AC method is only applicable if the quadratic has rational zeros, whereas the quadratic formula will always give you the solution, even if the roots are Complex.