Answer to Question #307956 in Calculus for Niu_bi

Question #307956

F(x) = 6x2 - 10x + 12


1
Expert's answer
2022-03-10T08:58:46-0500

Solution


Given that


f\left( x \right) = 6{x^2} - 10x + 12\


To solve, this f(x)=0f\left( x \right) =0


6x210x+12=06{x^2} - 10x + 12=0


3x25x+6=03{x^2} - 5x + 6=0


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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