Question

26. Find the quadratie polynomial whose zeroes are -9 and -1/9​

Answer 1

To find:-

• Quadratic polynomial.

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Solution:-

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Zero's or we can say roots of quadratic polynomial are -9 and -1/9.

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We know that,

♱$\large sum \: of \: zeros \: = \alpha + \beta = \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

So,

$\large sum \: of \: zeros \: = -9 + (\frac{ - 1}{9} ) = \frac{ - 82}{9}= \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} }$

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♱ $\large Product \: of \: zeros \: = \alpha \beta = \frac{constant\:term}{coefficient \: of \: {x}^{2} }$

So,

$\large Product \: of \: zeros \: = -9 \times (\frac{ - 1}{9}) = \frac{9}{9} = 1= \frac{constant\:term}{coefficient \: of \: {x}^{2} }$

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Therefore,

Sum of zero's = -82/9

Product of zero's = 1

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We know that,

If we have sum of zero's and product of zero's then the equation will be

⍈ x² - (Sum of zero's)x + (Product of zero's)

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So, Put the values

⇒x² - (-82/9)x + 1

⇒x² + 82/9x + 1

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Thus, Quadratic polynomial is x² + 82/9x + 1.