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Find the quadric polynomial whose zeroes …

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Find the quadric polynomial whose zeroes are 2+√3 And 2-√3

Posted by Jeevith Arumugam 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 5 years, 8 months ago

Since there are 2 zeroes, the polynomial is of degree 2.

Let a and b represents the zeroes of the polynomial.

Let {tex}a=2+\sqrt{3} and b=2-\sqrt{3}{/tex}

Since, the polynomial is of degree 2

Polynomial would be of the form {tex}{x^{2}-(a+b) x+a b} {/tex}

Therefore computing the values,

{tex}{a+b=(2+\sqrt{3})+(2-\sqrt{3})=4}{/tex}

{tex}{a b=(2+\sqrt{3}) \times(2-\sqrt{3})=4-3=1}{/tex}

Therefore, the polynomial is {tex}{x^{2}-4 x+1} {/tex}

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