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How do you find the discriminant and number of real solutions to a quadratic equation?
To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, you use the formula Δ = b^2 - 4ac. The discriminant helps determine the nature of the roots: if Δ > 0, there are two distinct real roots; if Δ = 0, there is one real root (a repeated root); and if Δ < 0, there are no real roots (two complex conjugate roots). The number of real solutions is directly related to the discriminant's value.
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BlakeThe equation ax^2 + bx + c = 0 where a, b and c are real and a is non-zero has discriminant D = b^2 – 4ac. Then,
- if D > 0 the equation has two real roots which are distinct;
- if D = 0 the equation has two real roots which are coincident;
- if D < 0 the equation has two roots which form a complex conjugate pair (advanced mathematics only).
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What is the expression b2-4ac under the radical sign in the quadratic formula?
6
How do you know if a quadratic equation can be factored?
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.
Using the discriminant determine the number and type of solutions for this equation?
There are an indeterminate number of invisible solutions.
Explain why the roots of a quadratic equation are imaginary if the value of the discriminant is less than 0?
The square of any real number is non-negative. So no real number can have a negative square. Consequently, a negative number cannot have a real square root. If the discriminant is less than zero, the quadratic equation requires the square root of that negative value, which cannot be real and so must be imaginary.
The is the name of the number under the radical symbol in the quadratic formula?
discriminant
