Question

If yelfa & bitta are two zeros of the polynomial 25p^2-15p+2. Find the quadratic polynomial whos zeros are 1/2yelfa & 1/2bitta.

Answer 1

If alpha,beta are the two zeros of the polynomial 25p^2-15p+2=0

here alpha+beta=-b/a=-(-15)/25=3/5==>1

alpha . beta=c/a=2/25==>2
Now quadratic polynomial with zeros 1/2alpha,1/2beta is

x^2-(1/2alpha+1/2beta)x+(1/2alpha. 1/2 beta) =0

x^2-1/2(1/alpha+1/beta)x+1/4(1/alpha.beta)=0

x^2-1/2(alpha+beta/alpha.beta)x+1/4(1/(2/15))=0. { from 2 }

x^2-1/2((3/5)/(2/15))x+15/8=0. { from 1,2 }

x^2-1/2(9/2)x+15/8=0

x^2-9/4x+15/8=0

8x^2-18x+15=0

This is the required quadratic polynomial