Question

find zereos of polynomial 4√3 x^2 + 5x - 2√3 =0​

Answer 1

p(x) = 4√3x² + 5x - 2√3

==> 4√3x² + 8x - 3x - 2√3 = 0

==> 4x(√3x + 2) - √3(√3x + 2) = 0

==> (√3x + 2)(4x - √3) = 0

Case-1:

==> √3x + 2 = 0

==> x = -2/√3

==> x = $\sf -\dfrac{2\sqrt{3}}{3}$

Case-2:

==> 4x - √3 = 0

==> x = $\sf \dfrac{\sqrt{3}}{4}$

Hence, Zeroes of the given polynomial are $\sf -\dfrac{2\sqrt{3}}{3} \:$ and $\sf \dfrac{\sqrt{3}}{4}$

Answer 2

Answer: 4√3 x^2 + 5x - 2√3

= 4√3 x^2+8x-3x - 2√3

= 4x(√3x+2)-√3(√3x+2)

= (√3x+2)(4x-√3)

Roots = √3x+2 = 0

x = -2/√3

4x-√3 = 0

x = √3/4

Roots are -2/√3 and √3/4.