Factor and find the x intercepts : 4x^2-13x+3=0

Hope my words aren't too ugly ahhaha

4x2-13x+3=0 Two solutions were found : x = 1/4 = 0.250

x = 3

Step by step solution : Step 1 : Equation at the end of step 1 : (22x2 - 13x) + 3 = 0 Step 2 : Trying to factor by splitting the middle term

2.1 Factoring 4x2-13x+3

The first term is, 4x2 its coefficient is 4.

The middle term is, - 13x its coefficient is - 13.

The last term, "the constant", is + 3

Step-1 : Multiply the coefficient of the first term by the constant 4 • 3 = 12

Step-2 : Find two factors of 12 whose sum equals the coefficient of the middle term, which is - 13.

-12 + - 1 = - 13 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 12 and - 1

4x2 - 12x - 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors:

4x • (x-3)

Add up the last 2 terms, pulling out common factors:

1 • (x-3)

Step-5 : Add up the four terms of step 4:

(4x-1) • (x-3)

Which is the desired factorization

Equation at the end of step 2 : (x - 3) • (4x - 1) = 0 Step 3 : Theory - Roots of a product:

3.1 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:

3.2 Solve : x-3 = 0

Add 3 to both sides of the equation:

x = 3

Solving a Single Variable Equation:

3.3 Solve : 4x-1 = 0

Add 1 to both sides of the equation:

4x = 1

Divide both sides of the equation by 4:

x = 1/4 = 0.250