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Please help I don't know how to do this

Please help I don't know how to do this-example-1

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\huge\bold\orange{QUESTIONS:}

3. Given this quadratic equation, 2x²-x-28= 0.

(a) List the factors of this equation.

(b) Determine the x-intercepts


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\huge\bold\orange{ANSWER:}

(a) (x-4) and (2x+7)

(b) x=4 and x=-7/2


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\huge\bold\orange{SOLUTION:}

  • 2x²-x-28=0
  • 2x²+7x-8x-28=0
  • 2x²-8x+7-28=0
  • 2x(x-4)+7(x-4)=0
  • (x-4)(2x+7)=0
  • x-4= 0 or 2x+7=0
  • x=4 or 2x=-7
  • x=4 or x= -7/2


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User Soriyyx
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3 votes

Answer:

(a) (2x +7), (x -4)

(b) (-7/2, 0), (4, 0)

Explanation:

(a)

When looking for integer factors of a quadratic of the for ax² +bx +c = 0, it is useful to start by looking for factor pairs whose product is a·c and whose sum is b.

Here, that means you're examining the factors of 2·(-28) = -56, and looking for a pair that have a sum of -1. We can start by examining the ways that -56 can be factored:

-56 = -56(1) = -28(2) = -14(4) = -8(7)

Sums of these factor pairs are -55, -26, -10, -1, so it is the last pair we're interested in.

At this point, you can rewrite the x-term using these factors and then factor the quadratic by pairs.

2x² -8x +7x -28 = 0 . . . . . . . use -x = -8x+7x

(2x² -8x) +(7x -28) = 0 . . . . group into pairs of terms

2x(x -4) +7(x -4) = 0 . . . . . . factor each pair of terms

(2x +7)(x -4) = 0 . . . . . . . . . the factored equation

The factors of this equation are (2x +7) and (x -4).

__

(b)

The x-intercepts are the values of x that make the factors zero.

2x +7 = 0 . . . looking for x that makes the first factor zero

2x = -7 . . . . . subtract 7

x = -7/2 . . . . divide by the coefficient of x

__

x -4 = 0 . . . . looking for x that makes the second factor zero

x = 4 . . . . . . add 4

The x-intercepts are x = -7/2 and x = 4.

User Mathifonseca
by
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