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16-12-2020
Mathematics

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The product of the roots of 2x^2 - 7x + N = 0 is -5. Find N.

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LammettHash LammettHash

16-12-2020

Let a and b be the roots of 2x² - 7x + N. Then

2x² - 7x + N = 2 (x - a) (x - b)

2x² - 7x + N = 2x² - 2 (a + b) x + 2ab

so that

2 (a + b) = 7

2ab = N

The product of the roots is ab = -5, so

N = 2 • (-5) = -10

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