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harkovskaia [24]
3 years ago
5

If alpha and beta are the zeroes of quadratic polynomial ax^2+bx+c , then find alpha^4+beta^4

Mathematics
1 answer:
weqwewe [10]3 years ago
5 0
Ill write A for alpha and B for beta.

AB = c/a  and A + B = -b/a

A^4 + B^4 = (A^2 + B^2)^2  -   2A^2B^2

                 = [(A + B)^2 - 2AB] ^2 - 2A^2B^2

Plugging in the values for A+B and AB we get

A^4 + B^4 = [(-b/a)^2 - 2c/a]^2 - 2(c/a)^2

   =    (b^2 / a^2 - 2c / a)^2 - 2c^2/a^2

  = (b^2 - 2ac)^2  - 2c^2
     ----------------      -----
          a^4                a^2

 =   (b^2 - 2ac)^2 - 2a^2c^2
       -----------------------------
                   a^4
            
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Step-by-step explanation:

Since Toby exercise 14hours a week, and John exercises 20% more than Toby

John increment in number of hours compared to Tobi will be;

20/100 ×14 = 2.8hrs

This shows John exercises 2.8hrs more than Tobi. Total number of hours exercised by John will become;

14+2.8 = 16.8hrs

Since Jenny exercises two more hours than John, Total number of hours exercised by Jenny will be;

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= 18.8hrs/week

If Jenny exercise 18.8hrs in a week, it means she will exercise 18.8×w/1 in w weeks which gives 18.8w weeks.

5 0
2 years ago
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Answer:

The answer is "k=k_1k_{2}^2"

Step-by-step explanation:

For point 1:

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For point 2:

2 \times(2\ NO\ (o)+O_2 \ (g)  \leftrightharpoons  2NO_2\ (g)) ..................K_2\\\\

Adding k_1 equation and  multiply by 2 in the equation k_2 so we get  \to 4NH_3\ (g) +7 O_2\ (g) \leftrightharpoons 4 NO_2\(g) +6H_2O\ (g)....... k\\\\k= k_1\times k_{2}^2\\\\k=k_1k_{2}^2\\\\

3 0
2 years ago
Using the quadratic equation formula to solve 7x^2-x=7, what are the values of x
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quadratic formula:

x = <u>-b ± √(b² - 4ac)</u>

             2a

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subtract 7 from both sides:

7x² - x - 7 = 0

plug values into the quadratic formula:

x = <u>-(-1) ± √((-1)²- 4(7)(-7))</u>

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x = <u>1 ± √(197)</u>

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3 years ago
What is the scale factor of AABC to A DEF?
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4 0
2 years ago
A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire
Dafna11 [192]

Answer:

If length of the field is 30 ft, then width is 120 ft.

If the  length of the field is 60 ft, then width is 60 ft.

Step-by-step explanation:

Let us assume the length of the rectangular park = L ft

Let us assume the breadth of the rectangular park = B  ft

Now, AREA of the given park =  L x B

⇒ L x B  = 3,600 sq ft   ... (1)

Also, the perimeter of three sides  = 180 ft

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Now, from (1) and (2), we get:

L x B  = 3,600

2 L +  B  = 180   ⇒ B  = 180 - 2 L

Substitute this in(1) , we get:

L x B  = 3,600   ⇒ L x (180 - 2 L)  = 3600

\implies  180 L - 2L^2 = 3600\\\implies L^2 -90L + 1800 = 0\\\implies (L-30)(L-60)= 0

⇒ L = 30 or L  = 60

So, if L  = 30  ft , then B = 180 - 2L  =  180 - 60 = 120 ft

So, if L  = 60  ft , then B = 180 - 2L  =  180 - 120 = 60 ft

So, if length of the field is 30 ft, then width is 120 ft.

And if the  length of the field is 60 ft, then width is 60 ft.

4 0
3 years ago
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