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Why does a quadratic equation have two solutions when the value of its discriminant is positive?

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by mayaaang

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by mayaaang

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Example: = +5 and -5

Why?

(-5) (-5) = 25

(5) (5) = 25

Remember that the discriminant b² - 4ac is the radicand (under the square root symbol) in quadratic formula.

The quadratic formula:

- b +/-

x = -----------------------------------------

2a

Therefore if the value of discriminant is greater than zero or positive numbers, it has two roots or solutions.

Additional information on nature of roots/solution:

If the solution is greater than zero and a perfect square, there are two real, rational solutions.

If the solution is greater than zero but not a perfect square, there are two real, irrational solutions.

If the discriminant is equal to zero, there is only one real, rational solution

If the discriminant is less than zero, the solution is complex.