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For a quadratic equation f(x) = ax^2 + bx + c we can use the discriminant to find out how many roots (answers) the equation has.

To find this out we put it through b^2 - 4ac.

If the answer is smaller than 0 (negative) then there are no real roots.

If the answer is exactly 0 then there is one answer that is used twice.

If the answer is bigger than 0 then the equation has two different roots.

However, the discriminant cannot be used to give you the answer.

e.g. f(x) = x^2 + 1x + 2 The discriminant would equal -7 so you cannot solve that

f(x) = x^2 + 4x + 4 The discriminant would equal 0 so there is a repeated root. f(-2) = 0 and again f(-2) = 0

f(x) = 4x^2 + 10x + 6 The discriminant would equal 4 so there are two distinct roots. f(-3/2) = 0 and f(-1) = 0

A simple way of explaining why this works is that in the quadratic equation you have (b^2 - 4ac)^(1/2) and you cannot find the square route of of a negative number.


apex = The coefficient of the x2-term can't be 0, One side of the equation must be 0,

There can be no term whose degree is higher than 2.

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Q: What facts concerning the solution of a quadratic equation can be deduced from the discriminant of the quadratic formula?
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Related questions

If the discriminant of an equation is zero then?

The term "discriminant" is usually used for quadratic equations. If the discriminant is zero, then the equation has exactly one solution.

What do you find when you determine the discriminant?

Whether or not that there is a solution to a quadratic equation,

When will an equation have no solution?

If the discriminant of a quadratic equation is less than zero then it has no solutions.

If the discriminant of a quadratic equation equals zero what is true of the equation?

It has one real solution.

How can you have one solution in something that is quadratic?

b^2 - 4ac, the discriminant will tell you that a quadratic equation may have one real solution( discriminant = 0 ) , two real solutions( discriminant > 0 ), or no real solutions( discriminant < 0 ).

What type of equation is b2-4ac?


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.

Can a question on my maths have no solution?

Yes depending on the question for instance if the discriminant of a quadratic equation is less than zero then it will have no solutions.

Why do quadratic equations where the discriminant is 0 have exactly 1 real solution?

Suppose the quadratic equation is ax^2 + bx + c = 0 and D = b^2 - 4ac is the discriminant. Then the solutions to the quadratic equation are [-b ± sqrt(d)]/(2a). Since D = 0, the both solutions are equal to -b/(2a), a single real solution.

What solution does a negative discriminant have?

In basic mathematics, a quadratic equation with a negative discriminant has no solutions. However, at a more advanced level you will learn that it has two solutions which form a complex conjugate pair.

What is the discriminant of 8x2-2x plus 8 equals 0?

(-2)2-4*8*8 = -252 The discriminant is less than zero so there's no solution to the quadratic equation.

If the discriminant is negative the graph of a quadratic function will cross or touch the x-axis time s?

If the discriminant is negative, the equation has no real solution - in the graph, the parabola won't cross the x-axis.