Math, asked by magantiakshith440, 6 months ago

find a quadratic polynomial the sum and product of whose zeros are 1 and 1 respectively​

Answers

Answered by Anonymous
9

\huge\underline{ \mathbb\red{❥A} \green{n} \mathbb\blue{S} \purple{w} \mathbb \orange{E} \pink{r}} \:</p><p>

α+β=1

αβ=1

=k(x²-(α+β)x+αβ)

=k(x²-x+1)

polynomial is x²-x+1

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Answered by Anonymous
16

\sf\huge\blue{\underline{\underline{ Question : }}}

Find a quadratic polynomial whose the sum and product of zeros are 1 and 1 respectively.

\sf\huge\blue{\underline{\underline{ Solution : }}}

Given that,

  • \tt\red{:\implies Sum\:of\:the\:zeroes  :  \alpha + \beta = 1 }
  • \tt\red{:\implies Product\:of\:the\:zeroes : \alpha \beta = 1 }

To find,

  • Quadratic Polynomial.

Now,

We know that form of a quadratic polynomial is :

\tt\: x^{2} - (\alpha + \beta)x + \alpha\beta = 0

  • Substitute the zeroes.

\bf\:\leadsto x^{2} - (1)x + 1 = 0

\bf\:\leadsto x^{2} - x + 1 = 0

\underline{\boxed{\bf{\purple{ \therefore Quadratic\;Polynomial  :  x^{2} - x + 1 = 0.}}}}\:\orange{\bigstar}

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