What is an imaginary solution to a quadratic equation?

In relation to quadratic equations, imaginary numbers (and complex roots) occur when the value under the radical portion of the quadratic formula is negative. When this occurs, the equation has no roots (or zeros) in the set of real numbers.

How do you know if an equation has real or imaginary solutions?

The expression b2 − 4ac is called the discriminant, and can be used to determine whether the solutions are real, repeated, or complex: 1) If the discriminant is less than zero, the equation has two complex solution(s). 2) If the discriminant is equal to zero, the equation has one repeated real solution(s).

What does an imaginary solution mean?

The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x2 + 1 = 0. Although there is no real number with this property, i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication.

What are two imaginary solutions?

Write the quadratic equation in standard form. Add 5 to both sides of the equation.

  • Identify the values of a,b,and c.
  • Substitute the values of a,b,and c into the quadratic formula. Substitute 1 for a,2 for b,and 5 for c.
  • Simplify the radicand and the denominator. Use to simplify the square root.
  • Check each solution. We leave the check to you.
  • What are the methods of solving quadratic equations?

    List out the values of a,b and c.

  • Calculate the value of m by using the following equation: m=b/2a
  • Calculate the value of n using the following equation: n=c- (b²/4a)
  • Substitute your calculated values and value of a into the following equation: a (x+m)²+n
  • Equate your equation to 0 and thereby solve the equation.
  • How to solve imaginary equations?

    2 × 2 = 4

  • (−2) × (−2) = 4 (because a negative times a negative gives a positive)
  • 0 × 0 = 0
  • 0.1 × 0.1 = 0.01
  • What are imaginary solutions?

    Imaginary Numbers Definition.

  • Real And Imaginary Numbers.
  • Imaginary Numbers Chart.
  • Addition Of Numbers Having Imaginary Numbers.
  • Subtraction Of Numbers Having Imaginary Numbers.
  • Multiplication Of Numbers Having Imaginary Numbers.
  • Division Of Numbers Having Imaginary Numbers.
  • Fun Fact.
  • Solved Imaginary Numbers Examples