Question

Find all the zeroes of the polynomial 2x3 + x2 – 6x -3, if two of its zeros are -√3 and √3 .

Answer 1

Step-by-step explanation:

see the attachment.....

you can also do this by dividing given equation by x-√3 or x+√3 or x^2-3 .

Answer 2

★Solution:-

➠ Two zeroes of the polynomial are -√3 and √3.

➠ Now, (x + √3)(x - √3) is a factor of the p(x).

➠ It means that x² - 3 is a factor of 2x³ + x² - 6x - 3.

« By long division method »

⠀⠀⠀ ______________

x² - 3) 2x³ + x² - 6x - 3 ( 2x + 1

⠀⠀⠀⠀2x³⠀⠀⠀ - 6x

⠀⠀⠀⠀----------------------------

⠀⠀⠀⠀0x³ + x² - 0x - 3⠀

⠀⠀⠀⠀⠀⠀⠀ x²⠀⠀⠀- 3

⠀⠀⠀⠀----------------------------

⠀⠀⠀⠀⠀⠀⠀⠀⠀0

⠀⠀⠀⠀-----------------------------

➠ 2x + 1 = 0

➠ 2x = -1

➠ x = -1/2

★ Therefore all zeroes of this polynomial are -√3 , √3 and -1/2.