Studdy AI Logo
Math

QuestionFactor the quadratic function f(x)=x2+14x+48f(x)=x^{2}+14x+48 and find the value of xx that fits: x=−8;x=[?]x=-8 ; x=[?].

Studdy Solution

STEP 1

Assumptions1. The given quadratic function is f(x)=x+14x+48f(x)=x^{}+14 x+48 . We are required to solve this function by factoring3. One root of the function is given as x=−8x=-8
4. We need to find the other root of the function

STEP 2

The general form of a quadratic function is f(x)=ax2+bx+cf(x)=ax^{2}+bx+c. The roots of a quadratic function can be found by factoring the function into the form (x−p)(x−q)=0(x-p)(x-q)=0, where p and q are the roots of the function.

STEP 3

Given that one root is x=−8x=-8, we can write the function in the form (x+8)(x−q)=0(x+8)(x-q)=0.

STEP 4

We can find the value of q by comparing the given function f(x)=x2+14x+48f(x)=x^{2}+14 x+48 with the factored form (x+8)(x−q)(x+8)(x-q).

STEP 5

Expanding the factored form, we get x2+8x−qx−8qx^{2}+8x-qx-8q. This should be equal to the given function f(x)=x2+14x+48f(x)=x^{2}+14 x+48.

STEP 6

Comparing the coefficients, we have1. Coefficient of x2x^{2} 1=11=1
2. Coefficient of xx: 8−q=148-q=14
3. Constant term −8q=48-8q=48

STEP 7

olving the equation −q=14-q=14 for q, we get q=−14=−6q=-14=-6.

STEP 8

Substitute q=−6q=-6 into the equation −8q=48-8q=48 to check if it holds true.

STEP 9

Calculate the left-hand side of the equation −8q-8q.
−8q=−8(−6)=48-8q=-8(-6)=48

STEP 10

Since the left-hand side equals the right-hand side, q=−6q=-6 is indeed the other root of the function.
The number that belongs in the green box is -6.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord