Does the function f(x) = ax+b have a discriminant? If so, what is it?

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In summary, the discriminant of a quadratic function is a value calculated using the formula b^2-4ac that is used to determine the nature of the solutions of the function. It can be interpreted as positive, zero, or negative, which respectively correspond to two distinct real solutions, one real solution, or no real solutions. The discriminant can also be used to analyze the graph of a quadratic function and solve quadratic equations using the quadratic formula.
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Jhenrique
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f(x) = ax+b has discriminant? If yes, which is?
 
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Jhenrique said:
Nothing is said about the function of 1st degree...

So?...

They talk about polynomials of degree ##n##. So set ##n=1##.
 
  • #6
Second my calculus, the discriminant is 1. Correct?
 

FAQ: Does the function f(x) = ax+b have a discriminant? If so, what is it?

What is the discriminant of a quadratic function?

The discriminant of a quadratic function is a value that is used to determine the nature of the solutions of the function. It is calculated using the formula b^2-4ac, where a, b, and c are the coefficients of the quadratic function in the form ax^2 + bx + c.

How do you interpret the discriminant of a quadratic function?

The discriminant can be interpreted as follows:

  • If the discriminant is positive, the quadratic function has two distinct real solutions.
  • If the discriminant is zero, the quadratic function has one real solution (a double root).
  • If the discriminant is negative, the quadratic function has no real solutions (two complex solutions).

How can the discriminant be used to determine the nature of the solutions of a quadratic function?

The discriminant can be used to determine the nature of the solutions of a quadratic function by analyzing its sign. If the discriminant is positive, the quadratic function has two distinct real solutions. If it is zero, the function has one real solution. And if it is negative, the function has no real solutions.

What does the discriminant tell us about the graph of a quadratic function?

The discriminant can tell us about the graph of a quadratic function by indicating the number and type of solutions that the function has. If the discriminant is positive, the graph will have two x-intercepts. If it is zero, the graph will have one x-intercept (a point of tangency with the x-axis). And if the discriminant is negative, the graph will have no x-intercepts (it will not intersect with the x-axis).

Can the discriminant be used to solve a quadratic equation?

Yes, the discriminant can be used to solve a quadratic equation by using the quadratic formula. If the discriminant is positive, the formula will give two distinct real solutions. If it is zero, the formula will give one real solution. And if the discriminant is negative, the formula will give two complex solutions.

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