Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
Question:
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
$4 x^{2}-4 x+1$
Solution:
$4 x^{2}-4 x+1=0$
$\Rightarrow(2 x)^{2}-2(2 x)(1)+(1)^{2}=0$
$\Rightarrow(2 x-1)^{2}=0 \quad\left[\because a^{2}-2 a b+b^{2}=(a-b)^{2}\right]$
$\Rightarrow(2 x-1)^{2}=0$
$\Rightarrow x=\frac{1}{2}$ or $x=\frac{1}{2}$
Sum of zeroes $=\frac{1}{2}+\frac{1}{2}=1=\frac{1}{1}=\frac{-(\text { coefficient of } x)}{\text { coefficient of } x^{2}}$
Product of zeroes $=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}=\frac{\text { constant term }}{\text { coefficient of } x^{2}}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.