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I may only be in 8th grade but I am absolutely positive that all quadratic equations have 2 solutions.
No - They may have 0,1, or 2 answers
For example, the problem x^2 + 8x +16 = 0 has only one solution -4.
This is because the radical evaluates to 0 rendering the +/- sign irrelevant.
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How do you write quadratic equations using roots?
If the two roots are x = r1 and x = r2 then the quadratic equation is: (x - r1)(x - r2) = x2 - (r1 + r2)x + r1r2 = 0
Systems of equations with different slopes and different y-intercepts have no solutions?
No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.
How do you find maximum height when working with quadratic equations?
In a quadratic equation, the vertex (which will be the maximum value of a negative quadratic and the minimum value of a positive quadratic) is in the exact center of any two x values whose corresponding y values are equal. So, you'd start by solving for x, given any y value in the function's range. Then, you'd solve for y where x equals the middle value of the two x's given in the previous. For example:y = x24 = x2x = 2, -2y = (0)2y = 0Which is, indeed, the vertex of y = x2
How do you determine the number of real solutions to a quadratic equation?
Put the equation in the form ax2 + bx + c = 0. Replace a, b, and c in the quadratic formula: x = (-b (plus-or-minus) root(b2 - 4ac)) / 2a. Look at the term under the radical sign, which I wrote as "root" here. If b2 - 4ac is...Positive: the equation has two real solutions.Zero: the equation has one ("double") solution.Negative: the equation has two complex solutions (and therefore no real solution).
If the graphs of two linear equations in a system have the same slope the system has what kind of solution?
If they have the same slope, then there are two possibilities. First say they have the same slope and different y intercepts. This means they are parallel lines and there is no intersection. The solution is the empty set or we say there is no solution.If the y intercept is the same, then the two equations represent the same line. In this case there is an infinite number of solutions.
Most quadratic equations have?
two solutions
Most quadratic equations have what?
Two solutions
What are the two solutions for quadratic equations?
Quadratic curves only have two solutions when the discrimant is greater than or equal to zero.
Why quadratic equations have two solutions?
If the discriminant of b2-4ac of the quadratic equation is greater the 0 then it will have 2 solutions.
Can a system of two quadratic equations have two solutions?
Yes. It can have 0, 1, or 2 solutions.
Do you agree that quadratic equations has at most two solutions?
Yes and sometimes the two solutions are equal
Most quadric equations have?
A quadratic equation can have two real solutions, one real solution, or two complex solutions, none of them real.
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.
Why are there usually two solutions to a quadratic equation?
In the graph of a quadratic equation, the plotted points form a parabola. This parabola usually intersects the X axis at two different points. Those two points are also the two solutions for the quadratic equation. Alternatively: Quadratic equations are formed by multiplying two linear equations together. Each of the linear equations has one solution - multiplying two together means that the solution for either is also a solution for the quadratic equation - hence you get two possible solutions for the quadratic unless both linear equations have exactly the same solution. Example: Two linear equations : x - a = 0 x - b = 0 Multiplied together: (x - a) ( x - b ) = 0 Either a or b is a solution to this quadratic equation. Hence most often you have two solutions but never more than two and always at least one solution.
Do quadratic equations always have two real solutions?
No. A quadratic may have two identical real solutions, two different real solutions, ortwo conjugate complex solutions (including pure imaginary).It can't have one real and one complex or imaginary solution.
How many real solutions can the quadratic formula give?
A quadratic equation can have either two real solutions or no real solutions.
Do all quadratic equation have a solution?
No. Some have two solutions where as some have none.
