Question

2x⁴-7x³+3x²-5x+7÷x²-1​

Answer 1

Answer:

Step-by-step explanation:

When  f(x) has roots in the interval  [a,b]  then;

xn=∣b∣∣f(a)∣+∣a∣∣f(a)∣∣f(a)∣+∣f(b)∣  

Where  xn  is the root approximation.

Obviously this is a general formula that I made from the basics of linear interpolation which uses similar triangles to find the approximation by;

∣f(b)∣−xnxn−∣f(a)∣=∣f(b)∣∣f(a)∣  

This was the linear interpolation method…you can use it but here's Newton Raphson;

xn+1=xn−f(xn)f′(xn)  

Now let  f(x)=2x4−3x2+3x+1  

f(x)  changes sign in the interval.

Now I used a graphing application to show me a graph of f(x) and it has two real roots and both are negative. From trial and error I found that  f(x)  changes sign in the interval  [−0.3,−0.25]  

So let  x0=−0.25  

Then using the formula for Newton Raphson we get;

x1=−0.2660714286  

x2=−0.2659426044  

x3=−0.2659425963  

x4=−0.2659425963  

That's one solution…we are saying this since it is now not changing meaning we have come to the solution.

The other solution could be found finding the second interval in which  f(x)  changes sign which is  [−1.55,−1.5]  

So letting  x0=−0.5  the Newton Raphson method gives us;

x1=−1.508333333  

x2=−1.508224674  

x3=−1.508224656  

x4=−1.508224656  

So again it started repeating it's self so now we can conclude that the solutions to the equation  2x4−3x2+3x+1=0  are;

x≈−0.2659425963  

Or

x≈−1.508224656

hope it helps..

Answer 2

Answer:

Step-by-step explanation: