Two: one is 0, the other is -b/a
ax2 + bx + c = 0, but c = 0
⇒ ax2 + bx + 0 = 0
⇒ ax2 + bx = 0
⇒ x(ax + b) = 0
⇒ x = 0
or (ax + b) = 0 ⇒ x = -b/a
The answer depends on what the factors will be. For example, every quadratic can be factored if you allow complex numbers. If not, then it helps to use the discriminant. If it is positive, there are two real factors or solutions. If that positive number is a perfect square, then the factors are rational numbers. If not, they are real but not rational (irrational). If the discriminant is 0, there is one real solution. Lastly, if it is negative, there are no real solutions.
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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.
That is simple. Think about linear equation and graphs. Think about rise over run. Vertical rise up is positive, rise down is negative. (by Stephen Hawking)
An equation with absolute values instead of simple variables has twice as many solutions as an otherwise identical equation with simple variables, because every absolute value has both a negative and a positive counterpart.
They each typically have two solutions, a positive one and a negative one.
Two distinct real solutions.
The number of solutions for a quadratic equation corresponds to the points where the graph of the quadratic function intersects the x-axis. If the graph touches the x-axis at one point, the equation has one solution (a double root). If it intersects at two points, there are two distinct solutions, while if the graph does not touch or cross the x-axis, the equation has no real solutions. This relationship is often analyzed using the discriminant from the quadratic formula: if the discriminant is positive, there are two solutions; if zero, one solution; and if negative, no real solutions.
No. By definition, a quadratic equation can have at most two solutions. For a quadratic of the form ax^2 + bx + c, when the discriminant of a quadratic, b^2 - 4a*c is positive you have two distinct real solutions. As the discriminant becomes smaller, the two solutions move closer together. When the discriminant becomes zero, the two solutions coincide which may also be considered a quadratic with only one solution. When the discriminant is negative, there are no real solutions but there will be two complex solutions - that is those involving i = sqrt(-1).
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It depends on the discriminant value of the quadratic equation. If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution; and if it is negative, there are two complex conjugate solutions.
The term inside the square root symbol is called the radicand. There isn't a specific term for it based on its sign; whether it's positive or negative, it's still the radicand.I'm a little confused by your reference to the quadratic equation.If the radicand is negative, the root is an imaginary number, though that doesn't specifically have anything to do with the quadratic equation in particular.If the quantity b2 - 4ac is negative in the quadratic equation, the root of the quadratic equation is either complex or imaginary depending on whether or not b is zero.---------------------------Thank you to whoever answered this first; you saved me a bit of trouble explaining this to the asker :)However, in the quadractic equation, the number under the radical is called the discriminant. This determines the number of solutions of the quadratic. If the radicand is negative, this means that there are no real solutions to the equation.
The solutions to a quadratic equation on a graph are the two points that cross the x-axis. NB A graphed quadratic equ'n produces a parabolic curve. If the curve crosses the x-axis in two different points it has two solution. If the quadratic curve just touches the x-axis , there is only ONE solution. It the quadratic curve does NOT touch the x-axis , then there are NO solutions. NNB In a quadratic equation, if the 'x^(2)' value is positive, then it produces a 'bowl' shaped curve. Conversely, if the 'x^(2)' value is negative, then it produces a 'umbrella' shaped curve.
The answer depends on what the factors will be. For example, every quadratic can be factored if you allow complex numbers. If not, then it helps to use the discriminant. If it is positive, there are two real factors or solutions. If that positive number is a perfect square, then the factors are rational numbers. If not, they are real but not rational (irrational). If the discriminant is 0, there is one real solution. Lastly, if it is negative, there are no real solutions.
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A quadratic equation, typically in the form ( ax^2 + bx + c = 0 ), is a polynomial of degree two, which means its graph is a parabola. According to the Fundamental Theorem of Algebra, a polynomial of degree ( n ) has exactly ( n ) roots (solutions) in the complex number system. Therefore, a quadratic equation has two solutions, which can be real or complex, depending on the discriminant (( b^2 - 4ac )). If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution (a double root); and if it is negative, there are two complex 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.