258,099 views
22 votes
22 votes
Use the discriminant to determine the number of solutions to the quadratic equation −40m2+10m−1=0

User Nicholas Hunter
by
2.7k points

1 Answer

15 votes
15 votes

From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.

In first place, you must know that the roots or solutions of a quadratic function are those values ​​of x for which the expression is 0. This is the values ​​of x such that y = 0. That is, f (x) = 0.

Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c

The solutions of a quadratic equation can be calculated with the quadratic formula:


Solutions=\frac{-b+-\sqrt{b^(2) -4*a*c} }{2*a}

The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c

The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.

If the discriminant:

  • is positive: the quadratic function has two different real solutions.
  • equal to zero: the quadratic function has a real solution.
  • is negative: none of the solutions are real numbers. That is, it has no real solutions.

In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:

discriminant= 10² -4*(-40)*(-1)

Solving:

discriminant= 100 - 160

discriminant= -60

The discriminant is negative, so the quadratic function has no real solutions.

User Tomanow
by
2.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.