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13 November, 01:06

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

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  1. 13 November, 01:57
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    Hope my words aren't too ugly ahhaha
  2. 13 November, 03:46
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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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