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Find a Cubic Polynomial Whose Zeroes Are `1/2, 1 and -3.`

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Question

Find a cubic polynomial whose zeroes are `1/2, 1 and -3.` 

 

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Solution

If the zeroes of the cubic polynomial are a, b and c then the cubic polynomial can be found as  

`x^3 – (a + b + c)x^2 + (ab + bc + ca)x – abc`              .............(1) 

Let a = `1/2, b=14 and c=-3` 
Substituting the values in (1), we get 

`x^3-(1/2+1-3)x^2+(1/2-3-3/2)x-(-3/2)` 

⇒ `x^3-(-3/2)x^2-4x+3/2` 

`⇒ 2x^3+3x^2-8x+3` 

 

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Chapter 2: Polynomials - Exercises 2

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R.S. Aggarwal Mathematics [English] Class 10
Chapter 2 Polynomials
Exercises 2 | Q 4

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