Question

Find the quadratic polynomial whose zeroes are -2/root3 and root3/4

Answer 1

Hi ,

Let p and q are two roots of a

quadratic equation

Sum of the roots = -2√3 + ( -√3/2 )

p + q = ( -4√3 - √3 ) /2

= -5√3 / 2 ----( 1 )

Product of the roots = ( -2√3 ) ( -√3/2)

pq = 3 ----( 2 )

Required quadratic equation ,

x² - ( p + q ) x + pq = 0

x² - ( - 5√3/2 ) x + 3 = 0

x² + 5√3/2 x + 3 = 0

Multiply each term with 2 , we get

2x² + 5√3 x + 6 = 0

I hope this helps you.