Wilma and Greg were trying to solve the quadratic equation
\[x^2 + bx + c = 0.\]Wilma wrote down the wrong value of $b$ (but her value of $c$ was correct), and found the roots to be $1$ and $6.$ Greg wrote down the wrong value of $c$ (but his value of $b$ was correct), and found the roots to be $-1$ and $-4.$ What are the actual roots of $x^2 + bx + c = 0$?

The actual roots of are and

Wilma wrongly reported the roots as

Greg wrongly reported the roots as

To get the actual roots, since Greg's value of b was correct, and Wilma's value of c was correct, we then have the correct quadratic equation as

Therefore the actual roots are   and

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The roots are -2 and -3

Step-by-step explanation:

In the function x² + bx + c, a is equal to 1, then the factored form of this function is: (x - x1)*(x - x2) where x1 and x2 are the roots.

Wilma got the following expression:

(x - 1)*(x - 6) = x² - 6x - x + 6 = x² - 7x + 6, where '+6' is correct but '-7x' is incorrect.

Greg got the following expression:

(x + 1)*(x + 4) = x² + 4x + x + 4 = x² + 5x + 4, where '+5x' is correct but '+4' is incorrect.

Therefore the quadratic equation is: x² + 5x + 6. Its roots are:

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