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creativ13 [48]
3 years ago
9

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 h

as zeros.

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
3 0

Answer:

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

Step-by-step 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.  

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Answer:

AC = 8√3       AC = 7.65          

A = 43.17°       AB = 16.8

B = 46.83°      B = 27°

Step-by-step explanation:

FIRST TRIANGLE

by using pythagorus theorem:

Hypo² = Base² + height²

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AC² = 19² - 13²

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sin A = 13/19

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B = 180° - 133.17°

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<h3>SECOND TRIANGLE</h3>

TanФ = base/height

Tan 63° = 15 / AC

1.96 = 15/AC

AC = 15/1.96

AC = 7.65

AB² = AC² + BC²

AB² = 7.65² + 15²

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