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

Updated: 11/1/2022

Wiki User

7y ago

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.

Wiki User

7y ago