How many solutions does the equation 6x2−2x=−9 have?

1 Answer
Annie
Aug 26, 2016

No real solutions

Explanation:

If we look at the formula for solving a quadratic
x=−b±√b2−4ac2a we can see the determinant. b2−4ac

This is the bit that determines whether the equation has 2 real roots, 1 root or no real roots
If the determinant is greater than zero there are 2 real roots, if it is zero there is one solution ( the graph of the equation touches the x axis)
In this case b2−4ac=(−2)2−4⋅6⋅9=-212
There is no real number which is √−216

The graph of this equation does not cross the x axis

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