Factor completely 2n^2+ 5n + 2

Given the quadratic equation"

2n^2 + 5n + 2

a = 2

b = 5

c = 2

Factor completely.

Solution:

In order to factor the given quadratic equation completely, first we must think of two numbers that when added, the answer is 5, and when multiplied, the answer is 2. Hence, if we are unable to find the number, we will use the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a
x = −5 ± √(5^2 − 4(2)(2))/2(2)
x = −5 ± √(25 − 16)/4
x = −5 ± √(9)/4
x = −5 ± 3/4

Solve for + - separately.

x = -5 + 3 /4
x = -2/4
x = -½

x = -5 - 3 / 4
x = -8/4
x = -2

Final answer:

x = -½
x = -2