Question

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

Answer 1

First, you need to get delta which is b squared minus 4ac. If delta is higher than cero, the polynomial has two solutions, if it is less, the polynomial has no real solutions and if it is the same, it has one solution.
Although that is only for second grade ecuations

Answer 2

Answer:

One can determine the number of roots by seeing the degree of the  given polynomial.

Step-by-step explanation:

The number of roots can be determine by just seeing the highest power of the given equation.

Example,

1) for the equation  $x-4=0$

here, the highest power the equation is one. So, it will have one root.

Lets check it by simplify  $x-4=0 \Rightarrow x=4$

Hence, the equation has only one root namely x = 4.

2) Consider a quadratic equation,

$10t^2-t-3=0$

here, the highest power the equation is two.So, it will have two roots.

Lets check it by simplify using middle term splitting method,

$10t^2+5t-6t-3=0$

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

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

$\Rightarrow t=\frac{-1}{2}$ or $\Rightarrow t=\frac{3}{5}$

thus, the equation has two roots.

Hence, one can determine the number of roots by seeing the degree of the  given polynomial.