Zero(s) of polynomial  x3 − 5x2 + 8x − 4 is/are

To find the zeros of the polynomial x³ - 5x² + 8x - 4, we need to set the polynomial equal to zero and solve for x.

x³ - 5x² + 8x - 4 = 0

This is a cubic equation and solving it can be complex. However, we can try to factor the polynomial or use synthetic division to find the roots.

Unfortunately, this polynomial does not factor nicely, so we will have to use the cubic formula or numerical methods to find the roots.

The cubic formula is:

x = [ -b ± sqrt(b² - 4ac) ] / (2a)

However, this formula is for quadratic equations, and our equation is cubic. So, we need to use a more complex formula or numerical methods like the Newton-Raphson method or the bisection method to find the roots.

These methods are beyond the scope of this response, but you can use online calculators to find the roots of the equation.

Please note that the roots of the equation might be real or complex numbers.

To find the zeros of the polynomial x³ - 5x² + 8x - 4, we need to set the polynomial equal to zero and solve for x.

x³ - 5x² + 8x - 4 = 0

This is a cubic equation and solving it can be complex. However, one common method is to make an educated guess about one of the roots and then use synthetic division or polynomial division to reduce the polynomial to a quadratic, which is easier to solve.

In this case, by trying a few small integers, we can find that x = 1 is a root of the polynomial:

1³ - 51² + 81 - 4 = 1 - 5 + 8 - 4 = 0

So, x = 1 is a root of the polynomial.

Now, we can use synthetic division to reduce the polynomial. We write the coefficients of the polynomial (1, -5, 8, -4) and then bring down the 1:

1 | 1 -5 8 -4

 1  -4  4   0

The numbers on the bottom row give the coefficients of the reduced polynomial, which is x² - 4x + 4.

Setting this equal to zero gives us the quadratic equation:

x² - 4x + 4 = 0

This can be factored to give:

(x - 2)² = 0

So the roots of this equation are x = 2 (twice).

Therefore, the original polynomial has roots x = 1, 2, 2.