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Is it possible to have a quadratic function with one real zero and one imaginary zero why or why not?
ax2+bx+c=0 with a,b and c real discriminant D=b2-4ac if D >0 then there are 2 real zeros if D = 0 then there is one real zero if D<0 then there are two imaginary zeros There are no other possibility for D For further information search for fundamental theorem of algebra
Can you factor x2 plus 8x plus 64?
No because the discriminant is less than zero.
A complex number might not be a pure imaginary number?
True. Complex numbers have a real part and an imaginary part. If either one of these is zero, the complex number will be a pure real or a pure imaginary.
What are non complex numbers?
A non complex number is a number that does not have any imaginary component. An imaginary component is a non zero factor of the square root of -1, in other words, the imaginary number i.
How do you factor x squared plus 4x plus 5?
x^2 + 4x + 5 cannot be factored because its discriminant is less than zero.
If the discriminant is negative the equation has solutions?
As stated in the attached link, there are three possible discriminant conditions: Positive, Zero, or Negative. If the discriminant is negative, there are no real solutions but there are two imaginary solutions. So, yes there are solutions if the discriminant is negative. The solutions are imaginary, which is perfectly acceptable as solutions.
What kind of solution does an equation has if the discriminant is negative?
If the discriminant is negaitve, there are no "real" solutions. The solutions are "imaginary".
What is the discriminant of the polynomial below?
That depends on the values of the polynomial but in general:- If the discriminant is greater than zero it has 2 solutions If the discriminant is equal to zero then it has 2 equal solutions If the discriminant is less than zero it has no solutions
How do you know if a quadratic equation will have more than one solutions?
Write the quadratic equation in the standard form: ax2 + bx + c = 0 Then calculate the discriminant = b2 - 4ac If the discriminant is greater than zero, there are two distinct real solutions. If the discriminant is zero, there is one real solution. If the discriminany is less than zero, there are no real solutions (there will be two distinct imaginary solutions).
What is a discriminant and how does help to solve equations?
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
Why are there usually two solutions in quadratic equations and when do they only have one solution?
If the discriminant of the quadratic equation is greater than zero then it will have two different solutions. If the discriminant is equal to zero then it will have two equal solutions. If the discriminant is less than zero then it will have no real solutions.
If the discriminant is zero the equation has solutions?
It has 2 equal solutions
You can determine by the discriminant whether the solutions to the equation are real or numbers?
imaginary
What does the discriminant tell you?
The discriminant tells you how many solutions there are to an equation The discriminant is b2-4ac For example, two solutions for a equation would mean the discriminant is positive. If it had 1 solution would mean the discriminant is zero If it had no solutions would mean that the discriminant is negative
The discriminant determines how many solutions a quadratic equation will have and whether they are real or?
imaginary
The determines how many solutions a quadratic equation will have and whether they are real or imaginary?
discriminant
The discriminant determines how many a quadratic equation will have and whether they are real or imaginary.?
solutions
