What are the number and nature of the roots of a quadratic equation if the value of the discriminant is 36?

The nature of roots of a quadratic equation can be determined by the value of its discriminant (D). See table below:

So, if the value of discriminant of a quadratic equation is 36, the nature of the root (according to the above table) is "real". 36 is a positive number and perfect square.

The Quadratic Formula is formally stated as:

The formula of the discriminant is the expression underneath the radical: b²−4ac.

To get 36 as the value of the discriminant, here are the possible numbers to use:

• a = 1; b = -2; c = -8
• a = 1; b = 8; c = 7
• a = 2; b = 10; c = 8

And since is greater than 0, there are two (unequal) real solutions.

Using this Quadratic Formula Calculator and Solver, you'll easily get those solutions.

Plugging in the numbers above, the following are the two real solutions for each example:

• a = 1; b = -2; c = -8 (x = 4; x = -2)
• a = 1; b = 8; c = 7 (x = -1; x = -7)
• a = 2; b = 10; c = 8 (x = -1; x = -4)

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