Question

For what value of a is (x-5)a factor of x³-3x²+ax-10​

Answer 1

SOLUTION

Given,

x-5 is a factor

=) x-5= 0

=) x= 5

Putting the value of x in equation

$= > {x}^{3} - 3 {x}^{2} + ax - 10 \\ = > {5}^{3} - 3 {(5)}^{2} + a(5) - 10 = 0 \\ = > 125 - 75 + 5a - 10 = 0 \\ = > 125 - 85 + 5a = 0 \\ = > 40 + 5a = 0 \\ = > 5a = - 40 \\ = > a = - \frac{40}{5} = - 8$

hope it helps ☺️

Answer 2

Step-by-step explanation:

Let, f (x) = x³ - 3x² + ax - 10 be the given polynomial.

By factor theorem,  If (x – 5) is a factor of f (x) then f (5) = 0  :

Now,

f (x) = x³ - 3x² + ax - 10

=> f (5) = (5)³– 3 (5)² + a (5) – 10

=> 0 = 125 - 3 × 25 + 5a - 10

=> 0 = 125 – 75 + 5a – 10

=> 0 = 5a + 40

=> -5a = 40

=> a = - 40/5

=> a = - 8

Hence, (x – 5) is a factor of f (x), if a = - 8.

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