# What are the x and y intercepts of the curve 3x^2-x+8=0?

Feb 21, 2017

There is no $x$-intercept and $y$-intercept is at $\left(0 , 6\right)$.
For $x$-intercept put $y = f \left(x\right) = 0$ i.e. $3 {x}^{2} - x + 6 = 0$
but as discriminant is ${b}^{2} - 4 a c = {\left(- 1\right)}^{2} - 4 \times 3 \times 6 = - 71$, we do not have a real solution and hence there is no $x$-intercept. Also observe that $3 {x}^{2} - x + 6 = 3 {\left(x - \frac{1}{6}\right)}^{2} + \frac{71}{12}$ and hence for all values of $x$, $3 {x}^{2} - x + 6 > 0$ and hence no $x$-intercept.
For $y$-intercept, we should put $x = 0$ and then $y = f \left(0\right) = 6$ and $y$-intercept is at $\left(0 , 6\right)$