Question

Find all the zeroes of the
polynomial
3 2
p(x)= 2x +x-6x-3 if two of its
zeroes are
-V3 and √3.​

Answer 1

f( x) = 2x³+ x² - 6x-3

Since the zeroes of f( x) are root 3 and -root 3 , the factors are x- root 3 and x+ root 3 respectively.

Therefore, ( x- root 3)× (x+

root 3)

= (x) ²- ( root 3) ²

= x²- 3

x²- 3 ) 2x³+ x²- 6x-3 ( 2x+1

2x³ - 6x

(–)_____(+)_______

x² -3

x² -3

___(-)____(+)_____

0 0

Therefore 2x+1=0

or, x= - 1/2

So, the zeroes of f(x) are

-root 3 , root 3 and -1/2.

Hope it helps you.

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