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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.

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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.

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

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

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 ).

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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.

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

Related questions

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

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

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

It has one real solution.

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 ).

6

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.

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

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 Â± sqrt(d)]/(2a). Since D = 0, the both solutions are equal to -b/(2a), a single real solution.

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.

(-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 equation has no real solution - in the graph, the parabola won't cross the x-axis.