Question

Factorise and find the zeros: x²-3√3+6

Answer 1

Answer:

Step-by-step explanation:

Between x^2 and 3root3x and 6, there is plus sign.

x^2 + 3root3 x + 6

= {x}^{2} + 3 \sqrt{3} x + 6 \\ \\ = {x}^{2} + 2\sqrt{3} x + \sqrt{3} x + 6 \\ \\ = x(x + 2 \sqrt{3} ) + \sqrt{3} (x + 2 \sqrt{3} ) \\ \\ = (x + 2 \sqrt{3} )(x + \sqrt{3} )

Answer 2

x² - 3√3x + 6

= x² - √3x - 2√3x + 6

= x(x - √3) - 2√3(x - √3)

= (x - √3)(x - 2√3)

=> x - √3 = 0 or x - 2√3 = 0

=> x = √3 or x = 2√3

Hence, the zeroes of the polynomial x² - 3√3x + 6 are √3 and 2√3.