Question

According to the Fundamental Theorem of Algebra, the graph of f(x) = x2 - 4x + 3, has roots. From the graph we can see that it has zeros.

Answer 1

2 roots

2 zeros

Explanation:

Answer 2

The graph
`f(x)=x^2-4x+3` has two zeros namely 3 and 1.

Explanation:

Consider the given equation of graph
`f(x)=x^2-4x+3`

According to the Fundamental Theorem of Algebra

For a given polynomial of degree n can have a maximum of n roots.

Thus, for the given equation
`f(x)=x^2-4x+3` the degree of polynomial is 2 , thus the function can have maximum of 2 roots.

We know at roots the value of function is 0 that is f(x) = 0,

Substitute f(x) = 0 , we get,
`f(x)=x^2-4x+3=0`

This is a quadratic equation,
`x^2-4x+3=0`

We first solve it manually and then check by plotting graph.

Quadratic equation can be solved using middle term splitting method,

here, -4x can be written as -x-3x,

`x^2-4x+3=0 \Rightarrow x^2-x-3x+3=0`

`\Rightarrow x(x-1)-3(x-1)=0`

`\Rightarrow (x-3)(x-1)=0`

Using zero product property,
`a\cdot b=0 \Rightarrow a=0\ or \ b=0`

`\Rightarrow (x-3)=0` or
`\Rightarrow (x-1)=0`

`\Rightarrow x=3` or
`\Rightarrow x=1`

Thus, the two zero of f(x) are 3 and 1.

We can also see on graph attached below that the graph
`f(x)=x^2-4x+3` has two zeros namely 3 and 1.