Select the values that are solutions to the inequality x2 + 3x – 4 > 0.

Question

Select the values that are solutions to the inequality x2 + 3x – 4 > 0.

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Mia 2 weeks 2021-09-09T12:37:00+00:00 2 Answers 0

Answers ( )

    0
    2021-09-09T12:38:07+00:00

    Answer:

    see explanation

    Step-by-step explanation:

    Solve the equation

    x² + 3x – 4 = 0 ← in standard form

    (x + 4)(x – 1) = 0 ← in factored form

    Equate each factor to zero and solve for x

    x + 4 = 0 ⇒ x = – 4

    x – 1 = 0 ⇒ x = 1

    The zeros are x = – 4 and x = 1

    These split the domain into 3 intervals, that is

    ( – ∞ , – 4), (- 4, 1), (1 , +∞)

    Choose a rest point in each interval, substitute into the quadratic and check the sign.

    x = – 5 : (- 5 + 4)(- 5 – 1) = (- 1)(- 6) = + 6 > 0

    x = 0 : (0 + 4)(0 – 1) = (4)(- 1) = – 4 < 0

    x = 5 : (5 + 4)(5 – 1) = (9)(4) = 36 > 0

    Hence x² + 3x – 4 > 0 has solution

    (- ∞, – 4) ∪ (1, + ∞ )

    0
    2021-09-09T12:38:22+00:00

    Answer is -6 and 5 on edge

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