Directions: Answer the question independently. Two friends tried solving a quadratic equation x2 + bx + c = 0. One started with the wrong value of b and got the roots as 4 and 14; the other started with the wrong value of c and got the roots as 17 and –2. Find the actual roots.

For the correct equation x2 + bx + c = 0, the sum of the roots gives -b and the product gives c. The first friend has the wrong b but the correct c, so c equals the product of 4 and 14, which is 56. The second friend has the wrong c but the correct b, so b equals the negative sum of 17 and -2, giving -15. The actual equation is x2 - 15x + 56 = 0, which factors to (x - 7)(x - 8) = 0, yielding the roots 7 and 8.

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