Question

Write an equation in which the quadratic expression 4x^2-26x+42 equals 0. Must show all work to receive credit.

Show the expression in factored form
Explain what your solutions mean for the equation in complete sentences.
HIGH POINT AND BRAIN LIST

Answer 1

a) 2(x - 3)(2x - 7) = 0

b) function is 0 when x = 3 or 7/2

Explanation:

4x² - 26x + 42 = 0

2(2x² - 13x + 21) = 0

2[2x² - 6x - 7x + 21] = 0

2[2x(x - 3) - 7(x - 3)] = 0

2(x - 3)(2x - 7) = 0

Solutions:.

x = 3, 7/2

Answer 2

(a) (x + 3)(2x + 7) = 0

(b) These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.

Explanation:

(a) We set 4x² -26x + 42 equal to 0:

4x² -26x + 42 = 0

Let's divide both sides by 2 to simplify this a bit:

2x² - 13x + 21 = 0

Now, we need factors a and b of 2 and c and d of 21 such that ac + bd = -13. The factors of 2 are: 1 and 2, so let's say a = 1 and b = 2. The factors of 21 are: (1, 21), (3, 7), (-1, -21), and (-3, -7). We see that if c = -7 and d = -3, this works:

ac + bd = 1 * (-7) + 2 * (-3) = -7 - 6 = -13

So, the factored form is:

(x - (-3))(2x - (-7)) = 0

(x + 3)(2x + 7) = 0

(b) So now we need to solve this. Set each of the two parenthetical expressions equal to 0:

x + 3 = 0

x = -3

AND

2x + 7 = 0

x = -7/2

These solutions mean that for these two x values, f(x) is equal to 0. It's also where the graph of f(x) crosses the x-axis.