Given:
|x^2 - 5x| = 1
This can be written as 2 equations:
x^2 - 5x = 1
x^2 - 5x - 1 = 0 ----- 1
x^2 - 5x = -1
x^2 - 5x + 1 = 0 ----- 2
Solving both quadratic equations would be time-consuming, and we don’t need the actual value of the roots. Hence, check the value of the discriminant i.e. b^ - 4ac
For equation 1, we get
5^2 - 4(1)(-1) = 21
For equation 2, we get
5^2 - 4(1)(1) = 25
When the discriminant is positive, the equation has 2 roots.
Since both equations have positive discriminants, the total number of x values satisfying the equation =
2+2 = 4
Answer: 4
Note: Properties of Discriminants -
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A positive discriminant indicates that the quadratic has two distinct real number solutions.
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A discriminant of zero indicates that the quadratic has a repeated real number solution.
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A negative discriminant indicates that neither of the solutions are real numbers.
[Source: https://www.khanacademy.org/]
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