Maths-
General
Easy

Question

x squared minus 6 x plus 7 equals 0
What is the sum of the solutions to the equation above?

The correct answer is: 6


    The general form of quadratic equation is a x squared plus b x plus c equals 0
    Solution to the quadratic equation using the quadratic formula is given by, x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
    Explanations:
    Step 1 of 3:
    The given quadratic equation is x squared minus 6 x plus 7 equals 0
    Here, a = 1, b = - 6 and c = 7.
    Step 2 of 3:
    The solution to the quadratic equation is given by,
    x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction
    not stretchy rightwards double arrow x equals fraction numerator negative left parenthesis negative 6 right parenthesis plus-or-minus square root of left parenthesis negative 6 right parenthesis squared minus 4 cross times 1 cross times 7 end root over denominator 2 cross times 1 end fraction
    not stretchy rightwards double arrow x equals fraction numerator 6 plus-or-minus square root of 36 minus 28 end root over denominator 2 end fraction
    not stretchy rightwards double arrow x equals fraction numerator 6 plus-or-minus square root of 8 over denominator 2 end fraction
    not stretchy rightwards double arrow x equals fraction numerator 6 plus-or-minus 2 square root of 2 over denominator 2 end fraction
    not stretchy rightwards double arrow x equals fraction numerator 2 left parenthesis 3 plus-or-minus square root of 2 right parenthesis over denominator 2 end fraction
    not stretchy rightwards double arrow x equals 3 plus-or-minus square root of 2
    The solutions to the quadratic equation are 3 plus square root of 2 and 3 minus square root of 2.
    Step 3 of 3:
    The sum of the solutions is given by,
    left parenthesis 3 plus square root of 2 right parenthesis plus left parenthesis 3 minus square root of 2 right parenthesis equals 3 plus 3 equals 6
    Final Answer:
    The sum of the solutions to the equation is 6.

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