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Find the zeros of the polynomial …

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Find the zeros of the polynomial 4x2_4x+1 and verify the relationship between zeros and co efficients

Posted by Wahith Meeran 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

We have,
f(x) = 4x²- 4x + 1
= 4x²- 2x -2x + 1
= 2x (2x - 1) - 1 (2x - 1)
= (2x - 1)(2x - 1)

Now f(x)=0 if 2x-1 =0

hence zeros of f(x) are {tex}\frac12{/tex} and {tex}\frac12{/tex}

sum of zeros = {tex} \frac { 1 } { 2 } + \frac { 1 } { 2 } = 1 {/tex}

product of zeros = {tex}\frac12{/tex} {tex}\times \frac12 =\frac14 {/tex}
In f(x) = 4x²- 4x + 1

a=4, b=-4,c=1

{tex}\style{font-family:Arial}{\style{font-size:14px}{\begin{array}{l}\text{sum of zeros=-}\frac ba=-\frac{-4}4=1\\\text{Product of zeros=}\frac ca=\frac14\end{array}}}{/tex}

Hence the relation of zeros and coefficients is verified.

0Thank You

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