Get the solution to "How do you find the roots for f(x)=x2+12x+20?"

High School
Algebra
Algebra I
Quadratic function and equation

kuntungw3

Answered question

2022-01-22

How do you find the roots for

f (x) = x^{2} + 12 x + 20

Answer & Explanation

Jaiden Conrad

Beginner2022-01-23Added 14 answers

Step 1
$f (x) = x^{2} + 12 x + 20$
Let $f (x) = 0$
$0 = x^{2} + 12 x + 20$
$0 = x^{2} + 2 \times 6 \times x + 6^{2} - 6^{2} + 20$
$0 = {(x + 6)}^{2} - 36 + 20 = {(x + 6)}^{2} - 16 ∣ + 16$
$16 = {(x + 6)}^{2} ∣ \sqrt{}$
$\pm \sqrt{16} = x + 6 ∣ - 6$
$- 6 \pm 4 = x_{1, 2}$
$x_{1} = - 2$ or $x_{2} = - 10$

Matias Lang

Beginner2022-01-24Added 10 answers

Step 1

f (x) = x^{2} + 12 x + 20

The roots are the x-intercepts. These occur where

f (X) = 0

NKS

0 = x^{2} + 12 x + 20

Now we can factor the right side. We need to find factors of 20 that when summed give us 12
Factors of 20:

(1, 20), (2, 10), (4, 5)

If we sum each pair, the one that gives us 12 is (2, 10)
Hence, we factor as:

0 = (x + 10) (x + 2)

So the factor as:

x + 10 = 0 \to x = - 10

x + 2 = 0 \to x = - 2

Hence:

x = - 10

x = - 2

RizerMix

Expert2022-01-27Added 656 answers

Step 1

f (x) = x^{2} + 12 x + 20 = 0

Find 2 real roots, that are both negative

(a c > 0; a b > 0)

, knowing their sum

(- b = - 12)

and their product

(c = 20)

.They are: -2 and -10Note: When

a = 1

, we don't have to do factoring by grouping and solving the 2 binomials.

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