This is the basic and conceptual question from polynomials in which we have given zeroes 1/2, 1 and -3 and we have to find the cubic polynomial
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 2B, question no 4
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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 1/2​,1 and –3
Let us say , a=1/2​,b=1 and c=−3
Putting the values of a,b and c in equation (1) we get :
=x³−(1/2+1−3)x²+(1/2​−3−3/2​)x−(−3/2​)
=x³−(−3)/2​x²−4x+3/2
=2x³+3x²−8x+3
which is required polynomial.