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  Mathematics (NTSE/Olympiad)  

Polynomial

Value of a Polynomial

How to calculate of find the value of a Polynomial Equation:  

For a polynomial f(x) = 3x2 – 4x + 2.
To find its value at x = 3; replace x by 3 everywhere. So, the value of f(x) = 3x2 – 4x + 2 at x = 3 is given by
f(3) = 3 × 32 – 4 × 3 + 2 = 27 – 12 + 2 = 17.

Similarly, the value of polynomial f(x) = 3x2 – 4x + 2,
(i) at x = –2 is f(–2) = 3(–2)2 –4(–2) + 2 = 12 + 8 + 2 = 22
(ii) at x = 0 is f(0) = 3(0)2 – 4(0) + 2 = 0 – 0 + 2 = 2
(iii) at x = 1/2 is f(1/2) = 3(1/2)2– 4(1/2) + 2 = 3/4 – 2 + 2 = 3/4

Example: Find the value of the polynomial 5x – 4x2 + 3 at: (i) x = 0 (ii) x = –1

Solution:  Let p(x) = 5x – 4x2 + 3.
(i) At x = 0, p(0) = 5 × 0 – 4 × (0)2 + 3 = 0 – 0 + 3 = 3
(ii) At x = –1, p(–1) = 5(–1) – 4(–1)2 + 3 = –5 – 4 + 3 = – 6


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NTSE Mathematics (Class X)

  • Trigonometry
  • Similar Triangles
  • Statistics
  • Quadratic Equation
  • Arithmetic Progressions
  • Application of Trigonometry
  • Circle
  • Co-ordinate Geometry
  • Area related to Circle
  • Surface Area & Volume
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NTSE Mathematics (Class IX)

  • Trigonometry
  • Similar Triangles
  • Statistics
  • Quadratic Equation
  • Arithmetic Progressions
  • Application of Trigonometry
  • Circle
  • Co-ordinate Geometry
  • Area related to Circle
  • Surface Area & Volume
  • Constructions
  • Probability

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