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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.
Solution
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"))`
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