Polynomials

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This can be solved by substituting all the values in the given equation. As simple as that!!

Polynomial Remainder Theorem

    x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b.
    1. 2.5
    2. -5.5
    3. 3.5
    4. 6.5

 

  • Correct Answer
    Choice B. -5.5

Explanatory Answer

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Detailed Solution

Let f(x) = x4 – ax3 + bx2 – cx + 8

f(1) = 4
1 – a + b – c + 8 = 4
–a + b – c = - 5 ...... Eqn (1)
f(–1) = 3
1 + a + b + c + 8 = 3
a + b + c = - 6 ...... Eqn (2)
Adding Equation (1) and (2) we have
2b = -11,
or b = -5.5
Answer choice (b)

Correct Answer: -5.5.



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