If the fundamental theorem of algebra is correct , then why i am bein taught discriminant less than 0 for quadratic equations mean no real roots ? (i m a 10th standard student who was taught about polynomials and quadratic equations)
3 Answers
see explanation
Explanation:
If the discriminant is less than zero, there are no real roots, meaning that the graph never crosses the xaxis.
Example:
This can also be seen from the graph
graph{x^22x+3 [10, 10, 5, 5]}
This is important because then you can stress the validity of claims that might come up in questions like this.

Prove that this function has no real roots.

The discriminant can be used to solve equations
Example:
The equation
has no real roots.
(a) Show that p satisfies
(b) Hence find the set of possible values of p.
This why everything about the discriminant is important
The fundamental theorem of algebra allows for the roots to be either real or complex.
Explanation:
The fundamental theorem of algebra states that a polynomial of degree
So it's entirely possible for an
Looking at the example in the other answer, the polynomial has degree
If the discriminant is
Explanation:
The discriminant is the quantity under the square root symbol in the quadratic formula.
The standard form for a quadratic equation:
To solve for
If
Example
Substitute
Plug the values for
Simplify.
Simplify the square root.
Apply
Solutions for
So if the discriminant is negative, the roots will not be real numbers.