The roots of x² + px + q = 0 are each 1 less than the roots of x² − 5x + 6 = 0. Then:

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Accepted Answer

p = −3, q = 2. The roots of x² − 5x + 6 = 0 are 2 and 3, so the new roots are 1 and 2. Their sum is 3 and their product is 2, giving x² − 3x + 2 = 0. Comparing with x² + px + q = 0 gives p = −3 and q = 2.

The roots of $x^{2} + p x + q = 0$ are each 1 less than the roots of $x^{2} - 5 x + 6 = 0$ . Then:

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The roots of x2+px+q=0 are each 1 less than the roots of x2−5x+6=0. Then:

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

The roots of $x^{2} + p x + q = 0$ are each 1 less than the roots of $x^{2} - 5 x + 6 = 0$ . Then: