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vladimir1956 [14]
3 years ago
10

Solve for the roots in the equation below. x4 + 3x2 - 4 = 0

Mathematics
1 answer:
fgiga [73]3 years ago
8 0
First, you need to rewrite the expression into binomial form, so you are working with two terms (as you world with a quadratic):
(x²)²-3(x²)-4=0
Now, you can place the x²s into brackets as the coefficient is now 1:
(x²  )(x²  )
Next, find out two numbers that add together to give you -3 and multiply to give -4 (these are the leftover integers after removing the x²s). These two numbers are -4 and 1.
Place the -4 and 1 into the brackets:
(x²-4)(x²+1)=0
Notice that the x²-4 is a difference of two squares, so can be further factorised into (x+2)(x-2)
This leaves you with a final factorisation of:
(x+2)(x-2)(x²+1)=0
Now we handle each bracket individually to obtain our four solutions for x:
x+2=0
x=-2
x-2=0
x=2
x²+1=0
x²=1
x=<span>±1</span>

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Nostrana [21]

Answer:

The equation that matches the function shown is option;

C. y = sin\left (\dfrac{1}{2} \cdot x\right)

Step-by-step explanation:

The given graph of the function is a sinusoidal graph

The values of 'x' and 'y' coordinates at the maximum, x-intercept and minimum points are given as follows;

x, {}      y

0    {}   0

π {}       1

2·π   {} 0

3·π {}    -1

4·π {}    0

We note that sin(π/2) = 1, sin(π) = 0 sin(3·π/2) = -1, and sin(4·π/2) = sin(2·π) = 0

Therefore;

y = the sine of half the x-value

Which is presented as follows;

y = sin\left (\dfrac{1}{2} \cdot x\right).

5 0
3 years ago
Solve the system of equations 4x + 8y = 4 and —2x – 7y = -11 by combining<br> the equations.
masya89 [10]

Answer:the answer is six

Step-by-step explanation:

6 0
3 years ago
What is the slope of a line parallel to the line containing (-6,1) and (3,-2)
timama [110]

Answer:

m = -\frac{3}{9}

Step-by-step explanation:

Use the following formula:

slope: m = (y_{2} - y_{1})/(x_{2} - x_{1})

Let:

(x_{1} , y_{1}) = (-6 , 1)\\ (x_{2} , y_ {2}) = (3 , -2)\\

Plug in the corresponding numbers to the corresponding variables:

m = \frac{-2 - 1}{3 - (-6)}\\\\m = \frac{-3}{3 + 6}\\\\m = \frac{-3}{9}

m = -\frac{3}{9} is your answer.

~

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