Question

find the zeroes of polynomial p(x)=4√3x²+5x-2√3 and verify the relation btw zeroes and coefficients ..

quick !!

Answer 1

Hi...dear...
here is your solution...
4√3 x^2 + 5x -2√3
=4√3 x^2 +(8-3)x -2√3

=4√3(√3x+2)-√3(√3x+2)

= (√3x+2) (4x-3)

x = -2/√3
x = √3/4

now, alpha + beta = -b/a

= -5/4√3

Sum of zeros = -2/√3 + √3/4
= -5/4√3

Alpha×beta = c/a

= -2√3/4√3

= -1/2

Product of zeros = -2/√3 × √3/4

= -2√3/4√3

= -1/2

...Hence verified..
Regards,#shubhendu

Answer 2

p(x)= 4root3x2 + 5x - 2root3 = 0

4root3x2 + 8x - 3x - 2root3 = 0

4x(root3x + 2) - root3(root3x + 2)

(4x - root3)(root3x + 2)

x = root3 / 4

x= - 2/root3