How many solutions does a quartic function have?

How many solutions does a quartic function have?

four
There will be four complex (real and imaginary) solutions, since it has a degree of four, to every quartic equation. Not every quartic equation will have four real roots. It could have 0, 1, 2, 3, or 4 real roots and imaginary roots making up the total of four.

What is the maximum number of solutions a quadratic can have?

The maximum number of solutions that an equation in quadratic form can have is 2.

Can a quartic function have 3 zeros?

So far, we have seen quartic graphs with one, two or four x-intercepts. It’s also possible to have zero or three x-intercepts, as shown below.

Can a quartic function have 3 roots?

There is no restriction (but the degree) on the number of real roots, though; it is possible that the polynomial of degree 4 has 3 real roots too, like x2(x−1)(x−2).

What can be maximum possible solution of a linear equation in one variable?

A linear equation in one variable has infinitely many solutions.

What is the minimum number of solutions a quadratic can have?

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b2 – 4ac), is positive, negative, or zero. This expression has a special name: the discriminant.

How many solutions are possible for a quadratic quadratic system of equations?

Quadratic-quadratic systems may have 0, 1, 2, 3, 4, or infinitely many solutions (if the quadratics are equivalent equations).

Can a quartic function have 4 zeros?

This function is zero for only one value of x , namely x=0 . By the Fundamental Theorem of Algebra, any quartic equation in one variable has exactly 4 roots – counting multiplicity.

Can a quartic function have 4 turning points?

Turning points are points where the graph changes from increasing to decreasing. Cubic graphs will have zero or two turning points. Quartic graphs will have one or three turning points.

Can a quartic function have 2 zeros?

Sample Answer: A quartic function can have 0, 1, 2, 3, or 4 distinct and real roots.

Can a quartic function have 1 zero?

This function is zero for only one value of x , namely x=0 . So in one sense you could say that it has one zero. By the Fundamental Theorem of Algebra, any quartic equation in one variable has exactly 4 roots – counting multiplicity.

What is an example of a quartic function?

Quartic Function: Definition, Example A quartic function is a fourth-degree polynomial: a function which has, as its highest order term, a variable raised to the fourth power. It can be written as: f (x) = a 4 x 4 + a 3 x 3 + a 2 x 2 +a 1 x + a 0.

How do you find the maximum value of a quadratic function?

We can determine the maxim or minimum value of the quadratic function using the vertex of the parabola (graph the quadratic function). The general form of a quadratic function is f(x) = ax 2 + bx + c. Here, if the leading coefficient or the sign of “a” is positive, then the graph of the quadratic function will be a parabola which opens up.

How do you find the degree of a quartic equation?

A quartic function has the general formula f (x)=ax^4+bx^3+cx^2+dx+e, and every quartic function has four solutions, which may or may not be real. In general, the degree of the polynomial is the number of solutions and the maximum number of real solutions. But actually the question is wrong. It should be quartic equation, not function.

Which polynomial can have maximum number of solutions?

Quartic polynomial can have maximum four solutions. It may be real or complex. In general, polynomial of degree n have maximum n number of solutions. This is fundamental theorem of algebra proved by Gauss.