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Why does the discriminant determine the number and type of the solutions for a quadratic equation?
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula.
Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
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If the discriminant of a quadratic equation is -4 how many solutions does the equation have?
If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.
When will an equation have no solution?
If the discriminant of a quadratic equation is less than zero then it has no solutions.
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.
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.
What is the discriminant for x2-4x-5 equals 0?
The discriminant is 36 which means the quadratic equation has two solutions which are 5 and -1
