Find the quadratic polynomial whose zeroes …

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Find the quadratic polynomial whose zeroes are 3+ √5 and 3_√5

Posted by Danish Roshan 4 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Rajan Kumar Pasi 4 years, 10 months ago

This also seems like you didn't learn chapter 4 in a better way.

{tex}\large{Question: \space Zeroes=3+\sqrt5 \space and \space 3-\sqrt 5,\space find\space the \space quadratic\space equation?}{/tex}

{tex}\large Solution:{/tex}

{tex}\large {For\space any\space quadratic\space equation,\space x^2+x\times(\alpha+\beta)+(\alpha\times\beta)=0\space }{/tex}

{tex}\large {Here,\space let\space\space\alpha=3+\sqrt5 \space\space\space\space,\space\space\space\space\beta=3-\sqrt5.\space }{/tex}

{tex}\large {Thus,\space\space\space\alpha+\beta=3+\sqrt5 +3-\sqrt5 = 6\space\space\space\space,\space\space and\space\space\alpha\times\beta=(3+\sqrt5)(3-\sqrt5)=3^2-\sqrt5 ^2=9-5=4.\space }{/tex}

{tex}\large {\therefore\space x^2+x\times(\alpha+\beta)+(\alpha\times\beta)=0\space }\\ \large {\implies\space x^2+x\times(6)+(4)=0\space }\\ \large {\implies\boxed{\space x^2+6x+4=0}\space }\\{/tex}

Now after seeing this, don't you think this is a very very simple thing to do.

0Thank You

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