How can you quickly determine the number of roots a polynomial will have by looking at the equation?

Solution:

Look at the leading term of the equation to determine the number of roots of a polynomial. A leading term is a term with the highest power. 

1. Consider the linear equation x - 4 = 0

The highest power of the equation is 1 and will have one root.

We can check it by simplification

x = 4

The equation has only one root x = 4.

2. Consider the quadratic equation

10t² - t - 3 = 0

The highest power of the equation is 2 and will have two roots.

We can check it by simplification using the middle term splitting method

10t² + 5t - 6t - 3 = 0

Taking out the common terms

5t (2t + 1) - 3 (2t + 1) = 0

(2t + 1) (5t - 3) = 0

t = -1/2 and t = 3/5

So the equation has two roots.

Therefore, we can determine the number of roots a polynomial will have by looking at the leading term of the equation.

How can you quickly determine the number of roots a polynomial will have by looking at the equation?

Summary:

We can quickly determine the number of roots a polynomial will have by looking at the leading term of the equation.