Determine between which consecutive integers the real zeros of f(x) = x2 – 3x + 1 are located. between -1&0, 0&1 and 2&3

between -1&0,0&1 and 1&2

b. between -2&-1, 0&1 and 1&2

d. between -2&1, 0&1 and 1&2

a.

c.

Please select the best answer from the choices provided

A

C

Oo

a) between -1&0, 0&1 and 2&3

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

.

This polynomial has roots such that , given by the following formulas:

In this question:

So

2.62 is between 2 and 3.

0.38 is between 0 and 1.

So the correct answer is:

a) between -1&0, 0&1 and 2&3

Step-by-step explanation:

Given the quadratic expression f(x) = x2 – 3x + 1, the real zero of the expression will be the roots of the equation and this can be gotten as shown below

f(x) = x² – 3x + 1

On factorizing the equation using the general fomula when f(x) = 0;

x = -b±√b²-4ac/2a

from the equation above, a = 1, b = -3, c = 1

x = -(-3)±√(-3)²-4(1)(1)/2(1)

x = 3±√9-4/2

x = 3±√5/2

x = (3+√5)/2 or x = (3-√5)/2

x = 2.62 and 0.38

since 2.62 is between 2&3 and 0.38 is between 0&1 and -1&0, the required answer will be -1&0, 0&1 and 2&3

the correct answer is d

hope this