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If the quadratic equation:ax^2 + bx + c has discriminant d
then its roots are x1 = [-b - sqrt(d)]/2a and x2 = [-b + sqrt(d)]/2a
If d > 0 then sqrt(d) is real and non-zero. As a result x1 and x2 are real and distinct.
If d = 0 then sqrt(d) = 0 and so x1 = x2 and both are real.
If d < 0 the sqrt(d) is imaginary so x1 and x2 form a complex conjugate pair.
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How do you know if a quadratic function is factorrable or not?
If its discriminant is less than zero it can't be factored.
How do you find the discriminant of a function?
To find the discriminant of a quadratic function, first express it in descending powers, thusax^2 + bx + c = 0 where a, b and c are real and a is non-zero.Then the discriminant is b^2 - 4ac
How many discriminant did this quadratic equation have -4j2 3j-280?
A quadratic equation has one discriminant.
How many times will the graph of a quadratic function cross or touch the x axis if the discriminant is zero?
Once.
What are quadratic equations with real roots?
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
What is the discriminant of a quadratic function?
The form of the quadratic is ax2+bx+c, so the discriminant is b2-4ac.
What determines if a quadratic function has no x-intercepts?
If the quadratic function is written as ax2 + bx + c, then it has no x-intercepts if the discriminant, (b2 - 4ac), is negative.
How do you know if a quadratic function is factorrable or not?
If its discriminant is less than zero it can't be factored.
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.
How do you find the discriminant of a function?
To find the discriminant of a quadratic function, first express it in descending powers, thusax^2 + bx + c = 0 where a, b and c are real and a is non-zero.Then the discriminant is b^2 - 4ac
How many discriminant did this quadratic equation have -4j2 3j-280?
A quadratic equation has one discriminant.
Could there be a quadratic function that has an undefined axis of symmetry?
Yes and this will happen when the discriminant of a quadratic equation is less than zero meaning it has no real roots.
How many times will the graph of a quadratic function cross or touch the x axis if the discriminant is zero?
Once.
What are quadratic equations with real roots?
If the discriminant of the quadratic equation is zero then it will have 2 equal roots. If the discriminant of the quadratic equation is greater than zero then it will have 2 different roots. If the discriminant of the quadratic equation is less than zero then it will have no roots.
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.
What is the definition of quadratic discriminant?
The discriminant of the quadratic equation: y = ax^2 + bx + c is b^2 - 4ac
What a short example of a maximum of quadratic function?
A quadratic of the form ax2 + bx + c has no maximum if a > 0: it gets infinitely large. If a = 0 then it is not a quadratic. If a < 0 then the quadratic does have a maximum, and it is -D/4a where D is the discriminant = b2 - 4ac
