The sum of a positive number and its reciprocal-related expression gives x + 16/x = 8 (x not equal to 0). When written in standard form, this is x^2 - 8x + 16 = 0. How many distinct real roots does it have?

Question

Accepted Answer

1. x^2 - 8x + 16 = (x - 4)^2 = 0 gives x = 4 (a repeated root). So there is exactly 1 distinct root.

The sum of a positive number and its reciprocal-related expression gives $x + \frac{16}{x} = 8 (x$ not equal to 0).
When written in standard form, this is $x^{2} - 8 x + 16 = 0$ .
How many distinct real roots does it have?

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More Class 10 Standard Form and Roots practice

The sum of a positive number and its reciprocal-related expression gives x+x16​=8(x not equal to 0).When written in standard form, this is x2−8x+16=0.How many distinct real roots does it have?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Standard Form and Roots practice

The sum of a positive number and its reciprocal-related expression gives $x + \frac{16}{x} = 8 (x$ not equal to 0).
When written in standard form, this is $x^{2} - 8 x + 16 = 0$ .
How many distinct real roots does it have?