We want to completely write the given equation and find the other root given that we know one of the roots. We will find that the value of q is 6, and the missing root is x = 3.
Here we have the quadratic equation:
x^2 - 5x + q = 0.
We know that a root of this equation is 2, this means that 2 is a solution, then we have:
2^2 - 5*2 + q = 0
4 - 10 + q = 0
q = 10 - 4 = 6
Then the equation is:
x^2 - 5x + 6 = 0
To find the other root we can solve the Bhaskara's formula, it will give:
[tex]x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*6} }{2*1} = \frac{5 \pm 1 }{2}[/tex]
From this the two solutions are:
Concluding; the value of q is 6, and the missing root is x = 3.
If you want to learn more about quadratic equations, you can read:
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