If x-3 and x-1/3 are both factors of of ax^2+5x+ab, then show that a=-3/2

Question

Mathematics

Taylor Morgan

11 May, 16:36

If x-3 and x-1/3 are both factors of of ax^2+5x+ab, then show that a=-3/2

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Broderick Rasmussen · Answer 1

Since x-3 and x-1/3 are factors

(x-3) (x-1/3) = x²-3x - (1/3) x+1 = x² - (10/3) x+1

to make - (10/3) x to 5x multiply by - (3/10) * 5 = - 3/2

- (3/2) (x-3) (x-1/3) = - (3/2) x²+5x-3/2

Now by comparing - (3/2) x²+5x-3/2 with ax^2+5x+ab

you can see that a = - 3/2