Question

plz solve fast.....​

Answer 1

Answer:

a=2

Step-by-step explanation:

x+a is a factor of 2x²+2ax+5x+10

therefore f(-a)=0;

substituting values,

2(-a)²+2(a)(-a)+5(-a)+10=0

2a²-2a²-5a+10=0

-5a+10=0

therefore a=2

Answer 2

Answer :

a = 2

Note :

★ Remainder theorem : If a polynomial p(x) is divided by (x - c) , then the remainder obtained is given as R = p(c) .

★ Factor theorem :

If the remainder obtained on dividing a polynomial p(x) by (x - c) is zero , ie. if R = p(c) = 0 , then (x - c) is a factor of the polynomial p(x) .

If (x - c) is a factor of the polynomial p(x) , then the remainder obtained on dividing the polynomial p(x) by (x - c) is zero , ie. R = p(c) = 0 .

Solution :

Here ,

The given polynomial is ;

2x² + 2ax + 5x + 10 .

Let the given polynomial is p(x) .

Thus ,

p(x) = 2x² + 2ax + 5x + 10

Since ,

(x + a) is a factor of the polynomial p(x) , thus the remainder obtained on dividing p(x) by (x + a) will be zero .

If x + a = 0 , then x = -a

Thus ,

=> R = 0

=> p(-a) = 0

=> 2•(-a)² + 2a•(-a) + 5•(-a) + 10 = 0

=> 2a² - 2a² - 5a + 10 = 0

=> -5a + 10 = 0

=> 5a = 10

=> a = 10/5

=> a = 2

Hence , a = 2 .