F(x) = 6x2 - 10x + 12
Solution
Given that
f\left( x \right) = 6{x^2} - 10x + 12\
To solve, this
x = \frac{{ - \left( { - 5} \right) \pm \sqrt {{{\left( { - 5} \right)}^2} - 4\left( 3 \right)\left( 6 \right)} }}{{2\left( 3 \right)}}\
x = \frac{{5 \pm \sqrt {25 - 72} }}{6}\
x = \frac{{5 \pm \sqrt { - 47} }}{6}\
x = \frac{{5 + i\sqrt {47} }}{6}\ and x = \frac{{5 - i\sqrt {47} }}{6}\
Therefore, there are two imaginary solutions.
This has been shown by the following plot, which shows that the curve does not cross the x-axis. Hence no real solutions.
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