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Find the sum of the roots of the quadratic equation 6 − x − x2 = 0.

Mathematics

ScanSolve AI Answer

Answer

C

Step-by-step solution

3 steps

To find the sum of the roots of a quadratic equation, we first write the equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0. The sum of the roots is given by the formula −ba-\frac{b}{a}.

  1. Rewrite the given equation in standard form.

    The given equation is 6−x−x2=06 - x - x^2 = 0.
    Rearranging the terms to match ax2+bx+c=0ax^2 + bx + c = 0:
    −x2−x+6=0-x^2 - x + 6 = 0
    To make the leading coefficient positive, we can multiply the entire equation by -1:
    x2+x−6=0x^2 + x - 6 = 0

  2. Identify the coefficients aa, bb, and cc.

    From the equation x2+x−6=0x^2 + x - 6 = 0, we have:
    a=1a = 1
    b=1b = 1
    c=−6c = -6

  3. Calculate the sum of the roots.

    The roots are cc and kk, so their sum is c+kc+k.
    Using the formula for the sum of the roots:

    c+k=−bac+k = -\frac{b}{a}

    Substitute the values of aa and bb:

    c+k=−11c+k = -\frac{1}{1} c+k=−1c+k = -1

    The sum of the roots is -1.

    Comparing this with the given options:
    A. 2
    B. 1
    C. -1
    D. -3

    The correct option is C.

    The final answer is C. -1\boxed{\text{C. -1}}.

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