Question

find the zeroes of the polynomial f(x)= 4√3x^2+5x-2√3 , and show that : sum of zeroes = -5/4√3​

Answer 1

$\bold \red{Zeros \: of \: the \: given \: equation \: 4 \sqrt{3} x^{2}+5 x-2 \sqrt{3}=0 \text { is } \bold{-\frac{2}{\sqrt{3}} \text { or } \frac{\sqrt{3}}{4}}}$

To find:

Find zeros of given equation = ?

Solution:

Given: 4 root 3x square + 5x -2 root 3

The above given equation can be written as under:

$4 \sqrt{3} x^{2}+5 x-2 \sqrt{3}=0$

$4 \sqrt{3} x^{2}+8 x-3 x-2 \sqrt{3}=0$

$4 x(\sqrt{3} x+2)-\sqrt{3}(\sqrt{3} x+2)=0$

$(\sqrt{3} x+2)(4 x-\sqrt{3})=0$

$(\sqrt{3} x+2)=0 \text { or }(4 x-\sqrt{3})=0$

$\bold{x=-\frac{2}{\sqrt{3}} \text { or } \frac{\sqrt{3}}{4}}$