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Eva Campos
Mathematics
9 January, 08:12
Factor and find the x intercepts : 4x^2-13x+3=0
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Elvis Hicks
9 January, 08:36
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Hope my words aren't too ugly ahhaha
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Cohen Hardin
9 January, 08:37
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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
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