Question

x²+ax+15 and x²+3x-a have common factor x+5 then find the value of a?​

Answer 1

Answer:

a = 15/2

Step-by-step explanation:

Given x²+ax+15 and x²+3x-a have common factor x+5 .

x+5= 0 => x= -5

x²+3x-a = x²+ax+15

=> (-5)²+3(-5)-a = (-5)²+a(-5)+15

=> 25-15-a = 25-5a+15

=> 10-a = 40-5a

=> 5a-a =40 -10

=> 4a = 30

=> a = 30/4

=> a = 15/2

Therefore a = 15/2

Answer 2

Step-by-step explanation:

Given :-

x²+ax+15 and x²+3x-a have common factor x+5

To find :-

Find the value of a?

Solution :-

Given polynomials are x²+ax+15 and x²+3x-a

Let P(x) = x²+ax+15

Let g(x) = x²+3x-a

Given factor = x+5

We know that

By Factor Theorem

If x+5 is a factor of P(x) then P(-5) = 0

If x+5 is a factor of g(x) then g(-5) = 0

So x+5 is a common factor of P)x) and g(x) then

=> P(-5) = g(-5)

=> (-5)²+a(-5)+15 = (-5)²+3(-5)-a

=> 25-5a+15 = 25-15-a

=> 40-5a = 10-a

=> 40-5a-10+a = 0

=> 30-4a = 0

=> 30 = 4a

=> a = 30/4

=> a = 15/2 or 7.5

Therefore, a = 15/2 or 7.5

Answer:-

The value of a for the given problem is 15/2 or 7.5

Used formulae:-

Factor Theorem:-

" Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice-versa".