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The general form of a quadratic equation is ax2 + bx + c = 0.

Mathematics

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Answer

B

Step-by-step solution

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To solve the equation 2x2−4x−6=02x^2 - 4x - 6 = 0 using the quadratic formula, we first identify the coefficients aa, bb, and cc.
The general form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0.
From the given equation, we have:
a=2a = 2
b=−4b = -4
c=−6c = -6

The quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

  1. Substitute the values of aa, bb, and cc into the quadratic formula.

    x=−(−4)±(−4)2−4(2)(−6)2(2)x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-6)}}{2(2)}

  2. Simplify the expression under the square root.

    x=4±16−(−48)4x = \frac{4 \pm \sqrt{16 - (-48)}}{4} x=4±16+484x = \frac{4 \pm \sqrt{16 + 48}}{4} x=4±644x = \frac{4 \pm \sqrt{64}}{4}

  3. Calculate the square root and simplify further.

    x=4±84x = \frac{4 \pm 8}{4}

  4. Find the two possible values for xx.

    x1=4+84=124=3x_1 = \frac{4 + 8}{4} = \frac{12}{4} = 3 x2=4−84=−44=−1x_2 = \frac{4 - 8}{4} = \frac{-4}{4} = -1

    So, the solutions are x=3x=3 or x=−1x=-1.

    Comparing this with the given options:
    a. x=2x=2 or x=−3x=-3
    b. x=3x=3 or x=−1x=-1
    c. x=1x=1 or x=−3x=-3
    d. x=−2x=-2 or x=3x=3

    The correct option is b.

    The final answer is b. x=3 or x=−1\boxed{\text{b. } x=3 \text{ or } x=-1}.

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