Question

Find the value of a such that (x-4) is a factor of 5x³-7x²-ax-28.

Answer 1

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Answer 2

Let, f (x) = 5x³ - 7x² - ax - 28 be the given polynomial.

By factor theorem,  If (x - 4) is a factor of f (x) then f (4) = 0  :

Now, f (x) = 5x³ - 7x² - ax - 28  

⇒f (4) = 5(4)³ - 7(4)² + a (4) - 28

⇒ 0 = 5 × 64 - 7 × 16 + 4a - 28

⇒ 0 = 320 - 112 + 4a - 28

⇒0 = 180 -  4a  

⇒5a = 180

⇒a = 180/5

⇒a = 45

Hence, (x – 4) is a factor of f (x), if a is 45.

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