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kupik [55]
3 years ago
11

What are the zeros of the polynomial equation f(x)=x^2-12x+20?

Mathematics
1 answer:
bagirrra123 [75]3 years ago
8 0
f(x)=x^2-12x+20\\\\\text{The zeros:}\\\\f(x)=0\to x^2-12x+20=0\\\\x^2-10x-2x+20=0\\\\x(x-10)-2(x-10)=0\\\\(x-10)(x-2)=0\iff x-10=0\ \vee\ x-2=0\\\\\boxed{x=10\ \vee\ x=2}
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HELP ASAP PLZ i need help !<br>help me :((
kodGreya [7K]

Answer:

(1) g[f(x)]=\frac{8x-1}{12x-4}

(2)  g^{-1}(x)=\frac{x+1}{(3x-2)}

(3)    x=\frac{9+\sqrt{129} }{6},  \frac{9-\sqrt{129} }{6}

Step-by-step explanation:

Given functions f(x) = (4x-1)

are                     g(x)=\frac{2x+1}{3x-1}

(1)  g[f(x)]=\frac{2(4x-1)+1}{3(4x-1)-1}

                =\frac{8x-2+1}{12x-3-1}

                =\frac{8x-1}{12x-4}

(2) for g^{-1}(x), rewrite the function g(x) in terms of an equation

y=\frac{2x+1}{3x-1}

Substitute y in place of x and x in place of y, then solve for y.

x=\frac{2y+1}{3y-1}

(3y-1)x = 2y+1

3xy - x = 2y + 1

3xy - 2y = x + 1

y(3x-2) = x + 1

y=(\frac{x+1}{3x-2} )

⇒ g^{-1}(x)=\frac{x+1}{(3x-2)}

(3)    f[g(x)]=(x-1)

       f[g(x)]=4[\frac{2x+1}{3x-1}] =(x-1)

⇒    \frac{(8x+4)-(3x-1)}{3x-1}=(x-1)

⇒    \frac{8x-3x+4+1}{3x-1}=(x-1)

⇒    \frac{5x+5}{(3x-1)}=(x-1)

⇒    5x+5=(3x-1)(x-1)

⇒    5x+5=3x^2-3x-x+1

⇒   5x+5=3x^2-4x+1

⇒   3x^2-9x-4=0

⇒    x=\frac{9\pm\sqrt{(-9)^2-4(-4)\times3} }{2\times3}

   x=\frac{9\pm\sqrt{81+48} }{6}

   x=\frac{9\pm\sqrt{129} }{6}

   x=\frac{9+\sqrt{129} }{6},  \frac{9-\sqrt{129} }{6}

4 0
3 years ago
Pick out the composite numbers from the following numbers:
Anna35 [415]

Answer:

35, 39, 44, 52, 55, 57, 60, 69

Step-by-step explanation:

Composite numbers have multiple factors other than 1 and itself.

7 0
3 years ago
The sum of these fractions is between which two whole numbers? 3 4/6 1 3/6    4&amp;5 5&amp;6 6&amp;7 or 7&amp;8
umka21 [38]
<span>3 4/6 +  1 3/6  = 4 7/6 = 5 1/6
5 1/6 is between 5 and 6

answer is </span><span>5&6 (second choice)</span>
8 0
4 years ago
3/2+(-6/5) what does this equal? Please help
34kurt

Answer:

3/10

Step-by-step explanation:

The first thing that you need to do is to find the common denominator of the two fractions. The least common multiple of 2 and 5 is 10, so we can express the new equation as 15/10-12/10=3/10. Hope this helps!

8 0
3 years ago
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A bag of nuts weighs 3 ounces and costs 50 cents. What is the unit price? Round to the nearest cent.
galina1969 [7]

Answer:

50 cents/3 ounces = 16.67 cents/ounce

Step-by-step explanation:

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