Respuesta :

CintiaSalazar

Taking into account the discriminant of a cuadratic function, values of c ​​less than[tex]-\frac{9}{4}[/tex] cause the quadratic equation  -x²+3x+c=0 to have no real number solutions.

Discriminant of a cuadratic function

The function f(x) = ax²  + bx + c with a, b, c real numbers and a ≠ 0, is a function  quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).

The following expression is called discriminant:

Δ= b²- 4×a×c

The discriminant determines the amount of  roots of the function. The roots are those values ​​of x for which the expression is 0, so it graphically cuts the x-axis.

Then:

  • If Δ <0 the function has no real roots and its graph does not intersect the x-axis.
  • If Δ> 0 the function has two real roots and its graph intersects the x-axis at two points .
  • If Δ = 0 the function has a real root and its graph intersects the x-axis at a single point that coincides with its vertex. In this case the function is said to have a double root.

Value of c

In this case, for the quadratic equation -x²+3x+c=0 you know:

  • a= -1
  • b= 3
  • c= c

If the function has no real roots, the discriminant is less than zero (Δ <0). This is: b²- 4×a×c < 0

Substituting the corresponding values, you  get:

3²- 4×(-1)×c < 0

Solving:

9 + 4×c < 0

4×c < -9

c< (-9)÷4

c< [tex]-\frac{9}{4}[/tex]

Finally, values of c ​​less than[tex]-\frac{9}{4}[/tex] cause the quadratic equation  -x²+3x+c=0 to have no real number solutions.

Learn more about the discriminant of a cuadratic function:

brainly.com/question/14477557

Otras preguntas