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4 June, 15:21

Factor and solve the following equation 2x^2 + x - 21 = 0.

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Answers (2)
  1. 4 June, 15:23
    0
    x = - 7/2 and 3

    Step-by-step explanation:

    Use foil. Solve for x.
  2. 4 June, 15:38
    0
    The factors are (2x + 7) (x - 3) and the solutions are - 3.5 and 3

    Step-by-step explanation:

    * Lets explain how to factor a trinomial in the form ax² ± bx ± c:

    - Look at the c term first.

    # If the c term is a positive number, then its factors r, s will both

    be positive or both be negative.

    # a has two factors h and k

    # The sum of c and a is b.

    # The brackets are (hx ± r) (kx ± s) where a = hk, c = rs and b = rk + hs

    # If the c term is a negative number, then either r or s will be negative,

    but not both.

    # a has two factors h and k

    # The difference of c and a is b.

    # The brackets are (hx + r) (kx - s) where a = hk, c = rs and b = rk - hs

    * Lets solve the problem

    ∵ The equation is 2x² + x - 21 = 0

    ∵ The general form of the equation is ax² + bx + c = 0

    ∴ a = 2, b = 1, c = - 21

    ∵ c is negative

    ∴ its factors r and s have different sign

    ∵ a = 2

    ∵ The factors of a are h, k

    ∵ 2 = 2 * 1

    ∴ h = 2 and k = 1

    ∵ - 21 = 7 * - 3

    ∴ r = 7 and s = - 3

    ∵ The brackets are (hx + r) (kx - s)

    ∴ 2x² + x - 21 = (2x + 7) (x - 3)

    ∵ 2x² + x - 21 = 0

    ∴ (2x + 7) (x - 3) = 0

    - Equate each bracket by 0

    ∴ 2x + 7 = 0 ⇒ subtract 7 from both sides

    ∴ 2x = - 7 ⇒ divide both sides by 2

    ∴ x = - 7/2 = - 3.5

    - OR

    ∴ x - 3 = 0 ⇒ add 3 to both sides

    ∴ x = 3

    ∴ The solutions are - 3.5 and 3

    * The factors are (2x + 7) (x - 3) and the solutions are - 3.5 and 3
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