An important and conceptual question from polynomials in which we have given zeroes 2,-3,4 and we have to find a cubic polynomial.
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2B, question no 3
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General Form of cubic polynomial whose zeroes are a. b and c is :
x³−(a+b+c)x²+(ab+bc+ca)x−abc..........(1)
To find : cubic polynomial whose zeroes are 2,−3 and 4
Let us say , a=2,b=−3 and c=4
Putting the values of a, b and c in equation (1) we get :
=x³−(2−3+4)x²+(−6−12+8)x−(−24)
=x³−3x²−10x+24
which is required polynomial.