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2 years ago

Let f(x)=x2+5x−36 . Enter the x-intercepts of the quadratic function in the boxes.

Mathematics

2 answers:

san4es73 [151]2 years ago

6 0

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x^2-5*x-(36)=0

Step by step solution: Step 1: Trying to factor by splitting the middle term

1.1 Factoring x2-5x-36

The first term is, x2 its coefficient is 1.
The middle term is, -5x its coefficient is - 5.
The last term, "the constant", is -36 

Step-1: Multiply the coefficient of the first term by the constant 1 • -36 = -36

Step-2: Find two factors of -36 whose sum equals the coefficient of the middle term, which is - 5.

-36 + 1 = -35 -18 + 2 = -16 -12 + 3 = -9 -9 + 4 = -5 That's it

Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
 x2 - 9x + 4x - 36

Step-4: Add up the first 2 terms, pulling out like factors :
 x • (x-9)
 Add up the last 2 terms, pulling out common factors :
 4 • (x-9)
Step-5: Add up the four terms of step 4 :
 (x+4) • (x-9)
 Which is the desired factorization

Equation at the end of step 1 : (x + 4) • (x - 9) = 0 Step 2 :Theory - Roots of a product :

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2 Solve : x+4 = 0

Subtract 4 from both sides of the equation :
 x = -4

Solving a Single Variable Equation :

2.3 Solve : x-9 = 0

Add 9 to both sides of the equation :
 x = 9

Nezavi [6.7K]2 years ago

3 0

Answer:

$x=-9\text{ or }x=4$

Step-by-step explanation:

We have been given a function and we are asked to find the x-intercept of our given function.

To find the x-intercepts of our given function we will equate our function formula with 0.

$x^2+5x-36=0$

Now let us factor out our given quadratic equation by splitting the middle term.

$x^2+9x-4x-36=0$

$x(x+9)-4(x+9)=0$

$(x+9)(x-4)=0$

$(x+9)=0\text{ or }(x-4)=0$

$x+9-9=0-9\text{ or }x-4+4=0+4$

$x=-9\text{ or }x=4$

Therefore, the x-intercepts of our given quadratic functions are $x=-9\text{ or }x=4$ .

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Let ​ f(x)=x2+5x−36 ​. Enter the x-intercepts of the quadratic function in the boxes.

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