Math  /  Algebra

Question1. What does it mean to find the zeros of
2. Find the zeros of f(x)=x2+9x+14f(x)=x^{2}+9 x+14 14=7×214=7 \times 2

Studdy Solution

STEP 1

1. The function f(x)=x2+9x+14 f(x) = x^2 + 9x + 14 is a quadratic polynomial.
2. Finding the zeros of a function means finding the values of x x that make the function equal to zero.
3. The quadratic can potentially be factored into two binomials.

STEP 2

1. Define what it means to find the zeros of a function.
2. Set the function equal to zero.
3. Factor the quadratic expression.
4. Solve for the values of x x that make the function zero.

STEP 3

Define what it means to find the zeros of a function. The zeros of a function f(x) f(x) are the values of x x for which f(x)=0 f(x) = 0 . These are the x x -intercepts of the graph of the function.

STEP 4

Set the function equal to zero. We need to solve the equation:
x2+9x+14=0 x^2 + 9x + 14 = 0

STEP 5

Factor the quadratic expression. We look for two numbers that multiply to 14 14 (the constant term) and add to 9 9 (the coefficient of the linear term). The numbers 7 7 and 2 2 satisfy this condition because:
7×2=14 7 \times 2 = 14 7+2=9 7 + 2 = 9
Thus, we can factor the quadratic as:
(x+7)(x+2)=0 (x + 7)(x + 2) = 0

STEP 6

Solve for the values of x x that make the function zero. Use the zero product property, which states that if a product of factors is zero, at least one of the factors must be zero. Set each factor equal to zero:
x+7=0orx+2=0 x + 7 = 0 \quad \text{or} \quad x + 2 = 0
Solve each equation:
x+7=0x=7 x + 7 = 0 \quad \Rightarrow \quad x = -7 x+2=0x=2 x + 2 = 0 \quad \Rightarrow \quad x = -2
The zeros of the function f(x)=x2+9x+14 f(x) = x^2 + 9x + 14 are x=7 x = -7 and x=2 x = -2 .

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