## When polynomial p(x)= x^4-2x^2+3x^2-ax+3a-7 is divided by x+1 it leaves the remainder as 19. find the value of a

Question

When polynomial p(x)= x^4-2x^2+3x^2-ax+3a-7 is divided by x+1 it leaves the remainder as 19. find the value of a

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1 month 2021-08-15T08:53:43+00:00 5 Answers 0 views 0

p(x) = x4 – 2×3 + 3×2 – ax + 3a – 7

Divisor = x + 1

x + 1 = 0

x = -1

So, substituting the value of x = – 1 in p(x),

we get,

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 = 5

Since, a = 5.

We get the polynomial,

p(x) = x4 – 2×3 + 3×2 – (5)x + 3(5) – 7

p(x) = x4 – 2×3 + 3×2 – 5x + 15 – 7

p(x) = x4 – 2×3 + 3×2 – 5x + 8

As per the question

,

When the polynomial obtained is divided by (x + 2),

We get, x + 2 = 0

x = – 2

So, substituting the value of x = – 2 in p(x), we get,

p(-2) = (-2)4 – 2(-2)3 + 3(-2)2 – 5(-2) + 8

⇒ p(-2) = 16 + 16 + 12 + 10 + 8

⇒ p(-2) = 62 Therefore, the remainder = 62.

p(x) = x4 – 2×3 + 3×2 – ax + 3a – 7

Divisor = x + 1

x + 1 = 0

x = -1

So, substituting the value of x = – 1 in p(x),

we get,

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 = 5

Since, a = 5.

We get the polynomial,

p(x) = x4 – 2×3 + 3×2 – (5)x + 3(5) – 7

p(x) = x4 – 2×3 + 3×2 – 5x + 15 – 7

p(x) = x4 – 2×3 + 3×2 – 5x + 8

As per the question

,

When the polynomial obtained is divided by (x + 2),

We get, x + 2 = 0

x = – 2

So, substituting the value of x = – 2 in p(x), we get,

p(-2) = (-2)4 – 2(-2)3 + 3(-2)2 – 5(-2) + 8

⇒ p(-2) = 16 + 16 + 12 + 10 + 8

⇒ p(-2) = 62 Therefore, the remainder = 62.

p(x) = x4 – 2×3 + 3×2 – ax + 3a – 7

Divisor = x + 1

x + 1 = 0

x = -1

So, substituting the value of x = – 1 in p(x),

we get,

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 = 5

Since, a = 5.

We get the polynomial,

p(x) = x4 – 2×3 + 3×2 – (5)x + 3(5) – 7

p(x) = x4 – 2×3 + 3×2 – 5x + 15 – 7

p(x) = x4 – 2×3 + 3×2 – 5x + 8

As per the question

,

When the polynomial obtained is divided by (x + 2),

We get, x + 2 = 0

x = – 2

So, substituting the value of x = – 2 in p(x), we get,

p(-2) = (-2)4 – 2(-2)3 + 3(-2)2 – 5(-2) + 8

⇒ p(-2) = 16 + 16 + 12 + 10 + 8

⇒ p(-2) = 62 Therefore, the remainder = 62.

### x=1

p(x)=x^4-2x^2+3x^2-ax+3a-7

0=(1)4-2(1)+3(1)-a(1)+3a-7

0=4-2+3-a+3a-7

0=2a-2

2=2a

### a=1

Step-by-step explanation:

p(x) = x4 – 2×3 + 3×2 – ax + 3a – 7

Divisor = x + 1

x + 1 = 0

x = -1

So, substituting the value of x = – 1 in p(x),

we get,

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 = 5

Since, a = 5.

We get the polynomial,

p(x) = x4 – 2×3 + 3×2 – (5)x + 3(5) – 7

p(x) = x4 – 2×3 + 3×2 – 5x + 15 – 7

p(x) = x4 – 2×3 + 3×2 – 5x + 8

As per the question

,

When the polynomial obtained is divided by (x + 2),

We get, x + 2 = 0

x = – 2

So, substituting the value of x = – 2 in p(x), we get,

p(-2) = (-2)4 – 2(-2)3 + 3(-2)2 – 5(-2) + 8

⇒ p(-2) = 16 + 16 + 12 + 10 + 8

⇒ p(-2) = 62 Therefore, the remainder = 62.