Polynomials Q2
Qn: Polynomials
(a) 2.5 (b) -5.5
(c) 3.5 (d) 6.5
x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4,
div...
Soln: Polynomials
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) ...
Soln: Polynomials
Adding Equation (1) and (2) we have
2b = -11,
or b = -5.5
Answer choice (b)
x4 – ax3 + bx2 – cx + 8 = 0 ...
of 4

Polynomials - Remainder Theorem

Given equation of which contains variables raised to the power 4, we use the remainder theorem to solve for that variable.
Published on: Mar 4, 2016
Published in: Education      
Source: www.slideshare.net


Transcripts - Polynomials - Remainder Theorem

  • 1. Polynomials Q2
  • 2. Qn: Polynomials (a) 2.5 (b) -5.5 (c) 3.5 (d) 6.5 x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b.
  • 3. Soln: Polynomials 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) x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b.
  • 4. Soln: Polynomials Adding Equation (1) and (2) we have 2b = -11, or b = -5.5 Answer choice (b) x4 – ax3 + bx2 – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b.