The zeroes of the polynomial 4x2 - 3 will be:

Explanation -

The zeroes of a polynomial are the values of x that make the polynomial equal to zero. For the polynomial 4x² - 3, we set the polynomial equal to zero and solve for x:

4x2 - 3 = 0

4x2 = 3

Dividing both sides by 4:

\(x^2 = \frac{3}{4}\)

Now, taking the square root of both sides:

\(x = \pm \sqrt{\frac{3}{4}}\)

Remember that the square root of a fraction breaks down into the square root of the numerator over the square root of the denominator:

\(x = \pm \frac{\sqrt{3}}{2}\)

Therefore, the zeroes of the polynomial 4x² - 3 are \(x = \frac{\sqrt{3}}{2} \ \ and \ \ x = -\frac{\sqrt{3}}{2}.\)