Question

One of the roots of the equation x^2−6x+q=0 is 4.5. Find the other root and the value of the coefficient q.

Answer 1

I hope this helps you

Answer 2

we will see that the value of q is 6.75, and the other solution is 1.5

How to solve the quadratic equation?

We have:

$x^2 - 6x + q = 0$

And we know that 4.5 is a solution, then:

$4.5^2 - 6*4.5 + q = 0\\\\-6.75 + q = 0\\\\q = 6.75$

So the equation is:

$x^2 - 6x + 6.75 = 0$

Then, if the other solution is x = k, the factorization will be:

$(x - 4.5)*(x - k) = x^2 - 6x + 6.75 \\\\x^2 - (4.5 + k)*x + k*4.5$

Then we must have:

$4.5 + k = 6\\k*4.5 = 6.75$

From any of these two we get:

k = 6 - 4.5 = 1.5

The other solution is x = 1.5

If you want to learn more about quadratic equations:

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