Question

Find the quadratic polynomial whose zeroes are `2/3` and `-1/4` Verify the relation between the coefficients and the zeroes of the polynomial. 

Answer 1

Let ∝ =`2/3 and β =-1/4` 

Sum of the zeroes `=(∝+ β)=2/3+(-1/4)=(8-3)/12=5/12` 

Product of the zeroes, `∝β=2/3xx(-1/4)=-2/12=-1/6` 

∴ Required polynomial =`x^2-(∝+ β)x+∝β=x^2-5/12x+((-1)/6)` 

                                  `=x^2-5/12x-1/6` 

Sum of the zeroes =5/12=`(-("Coefficient of x"))/(("Coefficient of "x^2))` 

Product of zeroes=`-1/6= ("Constant term") /(("Coefficient of x^2"))`