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Question 2: How can we find the real root of a polynomial with one variable? Also...

Question 2: How can we find the real root of a polynomial with one variable? Also discuss the Newton-Raphson method.

Expert Solution

You can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x.

Example 1: Find the roots of the polynomial equation:

Solution: Given polynomial equation

By factoring the quadratic: =

x(x+2) + 2(x+2) = 0 therefore, (x+2)(x+2)=0

Set each factor equal to zero: x+2 =0 or x+2 = 0

So, x=-2 or x=-2 . Both the roots are same, i.e. -2.

Example 2: Find the roots of the polynomial equation:

Solution: Given polynomial equation

By factoring the quadratic: =

x(2x(x + 3) + (x + 3)) = 0 therefore, x(2x + 1)(x + 3) = 0

Set each factor equal to 0: x = 0,2x+1 = 0,x+3 = 0

So, x = 0,x = ,x = -3. Zeroes of polynomial are ,-3,0.

Newton Raphson Method

The Newton-Raphson method (also known as Newton's method) is a way to quickly find a good approximation for the root of a real-valued function f(x)=0f(x)=0. It uses the idea that a continuous and differentiable function can be approximated by a straight line tangent to it.

venereology answered 5 hours ago

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