Form the polynomial whose zeroes are 6-3-3- 6-3-3

The correct option is C Sum of zeroes = 6+√(3)/3+6 √(3)/3 = 12/3 = 4 Product of zeroes = 6+√(3)/3×6 √(3)/3 = 11 Required polynomial = k[x^2 (sum of zeroes) ...

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Byju's Answer

Standard X

Mathematics

Relationship Between Zeroes and Coefficients of a Cubic Polynomial

Form the poly...

Question

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

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Solution

The correct option is B

Sum of zeroes = $\frac{6 + \sqrt{3}}{3} + \frac{6 - \sqrt{3}}{3}$ = $\frac{12}{3}$ = 4

Product of zeroes = $\frac{6 + \sqrt{3}}{3} \times \frac{6 - \sqrt{3}}{3}$ = 11

Required polynomial = k[ $x^{2}$ - (sum of zeroes) $x$ + product of zeroes]

= k[ $x^{2} - 4 x + \frac{11}{3}$ ]

If k = 3, polynomial = $3 x^{2} - 12 x + 33$

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Form the polynomial whose zeroes are 6+√33,6−√33

The correct option is B Sum of zeroes = 6+√33+6−√33 = 123 = 4 Product of zeroes = 6+√33×6−√33 = 11 Required polynomial = k[x2 - (sum of zeroes)x + product of zeroes] = k[x2−4x+113] If k = 3, polynomial = 3x2−12x+33

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