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Find the sum of the roots of the quadratic equation 6 − x − x2 = 0.
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Step-by-step solution
3 stepsTo find the sum of the roots of a quadratic equation, we first write the equation in the standard form . The sum of the roots is given by the formula .
Rewrite the given equation in standard form.
The given equation is .
Rearranging the terms to match :
To make the leading coefficient positive, we can multiply the entire equation by -1:
Identify the coefficients , , and .
From the equation , we have:
Calculate the sum of the roots.
The roots are and , so their sum is .
Using the formula for the sum of the roots:Substitute the values of and :
The sum of the roots is -1.
Comparing this with the given options:
A. 2
B. 1
C. -1
D. -3The correct option is C.
The final answer is .
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