Question

Find the polynomial whose zeroes are root 3by2 and minus root 3 by2

Answer 1

To form the polynomial :-

we have

$x = \frac{ \sqrt{3} }{2} \\ x = \frac{ - \sqrt{3} }{2}$


❇ Sum of zeros =


$\frac{ \sqrt{3} }{2} - \frac{ \sqrt{3} }{2}$

= 0

❇ Product of zeros =


$\frac{ \sqrt{3} }{2} \times \frac{ \sqrt{ - 3} }{2}$


$\frac{ - 3}{4}$


Now ,
to form polynomial

we have a formula

=> x² - ( sum of zeros ) x + ( product of zeros )

so,

${x}^{2} - 0x + ( \frac{ - 3}{4} )$


$4{x}^{2} - 3$

so,

Our required polynomial is :- 4x² - 3


@Altaf