Two pipes fill a tank. The faster pipe takes x hours and the slower one takes (x + 3) hours. A condition gives the equation x^2 - 5x + 6 = 0 for the faster pipe's time. If the faster pipe time must be a positive number of hours, which roots are valid?

Question

Accepted Answer

Both 2 and 3 are valid. x^2 - 5x + 6 = (x - 2)(x - 3) = 0 gives roots 2 and 3, both positive and hence valid times in hours.

Two pipes fill a tank. The faster pipe takes $x$ hours and the slower one takes $(x + 3)$ hours.
A condition gives the equation $x^{2} - 5 x + 6 = 0$ for the faster pipe's time.
If the faster pipe time must be a positive number of hours, which roots are valid?

Step-by-Step Solution

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More Class 10 Standard Form and Roots practice

Two pipes fill a tank. The faster pipe takes x hours and the slower one takes (x+3) hours.A condition gives the equation x2−5x+6=0 for the faster pipe's time.If the faster pipe time must be a positive number of hours, which roots are valid?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Standard Form and Roots practice

Two pipes fill a tank. The faster pipe takes $x$ hours and the slower one takes $(x + 3)$ hours.
A condition gives the equation $x^{2} - 5 x + 6 = 0$ for the faster pipe's time.
If the faster pipe time must be a positive number of hours, which roots are valid?