Answer to Question #307956 in Calculus for Niu_bi

Question

F(x) = 6x² - 10x + 12

Answer 1

Solution

Given that

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

To solve, this $f\left( x \right) =0$

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

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

$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.