The polynomial whose zeroes are 5-3-3-5-3-3 is -

Sum of zeroes = 5+√(3)/3+5 √(3)/3= 10/3 Product of zeroes = 5+√(3)/3×5 √(3)/3 = 5^2 (√(3))^2/9 = 25 3/9=22/9 Required polynomial f(x) = [(x^2 (sum of zeroe ...

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Standard X

Mathematics

Relationship between Zeroes and Coefficients of a Polynomial

The polynomia...

Question

The polynomial whose zeroes are $\frac{5 + \sqrt{3}}{3}, \frac{5 - \sqrt{3}}{3}$ is .

9x2-30x+22

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9x2+30x+22

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x2+30x+22

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Solution

The correct option is A 9x2-30x+22
Sum of zeroes = $\frac{5 + \sqrt{3}}{3} + \frac{5 - \sqrt{3}}{3}$ = $\frac{10}{3}$
Product of zeroes = $\frac{5 + \sqrt{3}}{3} \times \frac{5 - \sqrt{3}}{3}$
$= \frac{5^{2} - (\sqrt{3})^{2}}{9} = \frac{25 - 3}{9} = \frac{22}{9}$
Required polynomial $f (x) = [(x^{2} - (s u m o f z e r o e s) x + (p r o d u c t o f z e r o e s)]$
$\Rightarrow [(x^{2} - \frac{10}{3} x + \frac{22}{9}$ ] [Multiplying by 9]
$\Rightarrow f (x) = 9 x^{2} - 30 x + 22$

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The polynomial whose zeroes are 5+√33,5−√33 is .

The correct option is A 9x2-30x+22Sum of zeroes = 5+√33+5−√33= 103 Product of zeroes = 5+√33×5−√33 =52−(√3)29=25−39=229 Required polynomial f(x)=[(x2−(sum of zeroes)x+(product of zeroes)] ⇒[(x2−103x+229] [Multiplying by 9] ⇒f(x)=9x2−30x+22

The polynomial whose zeroes are $\frac{5 + \sqrt{3}}{3}, \frac{5 - \sqrt{3}}{3}$ is .