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. Given the polynomial, f(x)=x² + ax+3 is such that the remainder when divided byx-1 is three times the remainder when divided by x+1. Find the value of a​

User Jon Tan
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1 Answer

3 votes

Answer:

x² + ax + 3 is 2

Explanation:

To find the value of "a" in the polynomial f(x) = x² + ax + 3, we have the condition that the remainder when divided by (x-1) is three times the remainder when divided by (x+1).

To solve this problem, we can use the Remainder Theorem. According to the Remainder Theorem, if we divide a polynomial f(x) by (x - c), the remainder will be f(c).

So, let's divide the polynomial f(x) by (x - 1) and (x + 1) to find the remainder and set up an equation:

Dividing f(x) by (x - 1):

Remainder = f(1)

= (1)² + a(1) + 3

= 1 + a + 3

= a + 4

Dividing f(x) by (x + 1):

Remainder = f(-1)

= (-1)² + a(-1) + 3

= 1 - a + 3

= 4 - a

According to the given condition, the remainder when divided by (x - 1) is three times the remainder when divided by (x + 1):

a + 4 = 3(4 - a)

Now, let's solve this equation for "a":

a + 4 = 12 - 3a

4a = 8

a = 2

Therefore, the value of "a" in the polynomial f(x) = x² + ax + 3 is 2.

User Raeven
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