A and B solved a quadratic equation with the leading coefficient 1. In solving it, A made a mistake in the constant term and obtained the roots as (5, –3) while B made a mistake in the coefficient of x and obtained the roots as (1, –3). The correct roots of the equation are:
Question
A and B solved a quadratic equation with the leading coefficient 1. In solving it, A made a mistake in the constant term and obtained the roots as (5, –3) while B made a mistake in the coefficient of x and obtained the roots as (1, –3). The correct roots of the equation are:
Solution
The correct roots of the equation can be found by using the fact that the sum and product of the roots of a quadratic equation ax^2 + bx + c = 0 are given by -b/a and c/a respectively.
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For the roots obtained by A (5, -3), the sum of the roots is 5 - 3 = 2 and the product of the roots is 5*(-3) = -15. This gives us the equation x^2 - 2x - 15 = 0.
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For the roots obtained by B (1, -3), the sum of the roots is 1 - 3 = -2 and the product of the roots is 1*(-3) = -3. This gives us the equation x^2 + 2x - 3 = 0.
The correct roots of the equation are the ones that satisfy both equations. In this case, the correct roots are (1, -3).
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