The polynomial f(x)=x^4-2x^3+3x^2-9x+3a-7 when divided by x+1 leaves the remainder 19. Find the value of a. Also find the remainder when p(x) is divided by x+2
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Answered by
31
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remainder wen divided by x+2 is 66
remainder wen divided by x+2 is 66
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nikitajha400:
I have ans in my ans booklet a=11/3 and reminder =66
no its wrong
Are u sure bcz this is my child homework and I don't know any think about polynomial so plzz help and cnfrm
see in the solution i did 19-7 its 19-8 nd den the answer will come 11/3
Ooo thank u so much☺
Answered by
40
Hello Dear.
Here is the answer---
Given Polynomial ⇒
P(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7.
Divisor = x + 1
∴ x + 1 = 0
∴ x = -1
Thus,
P(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a - 7.
19 = 1 + 2 + 3 + a + 3a - 7
19 = 6 - 7 + 4a
4a - 1 = 19
4a = 20
⇒ a = 4
∴ Value of a is 4.
Now, the Polynomial will be ---→
P(x) = x⁴ - 2x³ + 3x² - (4)x + 3(4) - 7
P(x) = x⁴ - 2x³ + 3x² - 4x + 12 - 7
P(x) = x⁴ - 2x³ + 3x² - 4x + 5
Now, When this polynomial is divided by (x + 2), then,
x + 2 = 0
x = - 2
∴ P(-2) = (-2)⁴ - 2(-2)³ + 3(-2)² - 4(-2) + 5
⇒ P(-2) = 16 + 16 + 12 + 8 + 5
⇒ P(-2) = 57
Thus, Remainder will be 57.
Here is the answer---
Given Polynomial ⇒
P(x) = x⁴ - 2x³ + 3x² - ax + 3a - 7.
Divisor = x + 1
∴ x + 1 = 0
∴ x = -1
Thus,
P(-1) = (-1)⁴ - 2(-1)³ + 3(-1)² - a(-1) + 3a - 7.
19 = 1 + 2 + 3 + a + 3a - 7
19 = 6 - 7 + 4a
4a - 1 = 19
4a = 20
⇒ a = 4
∴ Value of a is 4.
Now, the Polynomial will be ---→
P(x) = x⁴ - 2x³ + 3x² - (4)x + 3(4) - 7
P(x) = x⁴ - 2x³ + 3x² - 4x + 12 - 7
P(x) = x⁴ - 2x³ + 3x² - 4x + 5
Now, When this polynomial is divided by (x + 2), then,
x + 2 = 0
x = - 2
∴ P(-2) = (-2)⁴ - 2(-2)³ + 3(-2)² - 4(-2) + 5
⇒ P(-2) = 16 + 16 + 12 + 8 + 5
⇒ P(-2) = 57
Thus, Remainder will be 57.
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