Question

find the value of a if (x -4) is a factor of 5x³-7x² - ax - 28​

Answer 1

Answer:

a = 45

Step-by-step explanation:

Let f(x) = $5x^{3} - 7x^{2} - ax - 28$

x - 4 = 0

∴ x = 4

Since x - 4 is a factor,

∴ f(4) = 0

f(4) = $5(4)^{3} - 7(4)^{2} - 4a - 28$

 0  = 64 * 5 - 7*16 - 4a - 28

 0  = 320 - 112 - 4a - 28

     [Divide throughout by 4]

80 - 28 - a - 7 = 0

45 - a = 0

a = 45

Answer 2

Step-by-step explanation:

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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