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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

9x2+30x+22

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x2+30x+22

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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]
$\Rightarrow f (x) = 9 x^{2} - 30 x + 22$

Suggest Corrections

Similar questions

Q. The polynomial whose zeroes are

\frac{5 + \sqrt{3}}{3}, \frac{5 - \sqrt{3}}{3}

is .

Form the polynomial whose zeroes are $\frac{6 + \sqrt{3}}{3}, \frac{6 - \sqrt{3}}{3}$

Find a quadratic polynomial whose zeroes are

$(\sqrt{3} + \sqrt{5})$ , $(\sqrt{5} - \sqrt{3})$

Q. Form the quadratic polynomial whose zeroes are :

3 - \sqrt{5}, 3 + \sqrt{5}

Q. The quadratic polynomial whose zeros are

3 + \sqrt{5}

and

3 - \sqrt{5}

Join BYJU'S Learning Program

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 .