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Reptile [31]
3 years ago
7

The polynomial p{x) = x4 -2x3 + 3x2 -ax+3a-7 when divided by x+1 leaves the remainder 19. Find the values of a. Also, find the r

emainder when p(x) is divided by x+ 2.
Mathematics
1 answer:
Mrrafil [7]3 years ago
5 0

Answer:

a = 5

Remainder when p(x) is divided by x+2 = 62

Step-by-step explanation:

Given:

P(x) = x⁴-2x³+3x²-ax+3a-7

When x+1 divides the polynomial p(x) the ramainder is 19.

Applying remainder theorem,

x = -1

p(-1) = 19

Substitute the x = -1 into the polynomial expression

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 = 19

4a-1 = 19

4a = 19+1

4a = 20

a = 20/4

a = 5.

Hence, a = 5

p(x) = x⁴-2x³+3x²-5x+8

If p(x) is divided by x+2,

Then the remainder is p(-2)

p(-2) = (-2)⁴-2(-2)³+3(-2)²-5(-2)+8

p(-2) = 16+16+12+10+8

p(-2) = 62

Hence the remaider when p(x) is divided by x+2 is 62

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Answer:

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Step-by-step explanation:

I'm assuming the system is \left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.:

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(4x^2-7)(x^2-1)=0

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x=\pm1

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y=2(\pm\sqrt{\frac{7}{4}})^2-3

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y=2(\pm1)^2-3

y=2(1)-3

y=2-3

y=-1

Therefore, x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}} and y=-1,\frac{1}{2}

The ordered pair solutions are (-\sqrt{\frac{7}{4}},0.5), (\sqrt{\frac{7}{4}},0.5), (-1,-1), and (1,-1).

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