Why is this answer wrong? (point of intersection between parabola and line)
Question:
Use the discriminant to determine the number of points of intersection of the line $y=3x+5$ and the quadratic functions $f(x)=3x^2-2x-4$. Solve to find the points of intersection.
Using the discriminant, I got $133$, which is a positive value; therefore there should be $2$ $x$-intercepts ($2$ intersections between parabola and line). Then calculating the zeros (in this case, points of intersection) using the quadratic formula, I got $x = 6.08876$ or $x = 2.24457$.
Apparently the right answer is $x = -1.089$ or $x = 2.755$
Can you please calculate if your answer matches up with any of the two versions? I don't know if it's just me or the textbook got it wrong.
Thank you!
$\endgroup$ 21 Answer
$\begingroup$You have computed the discriminant correctly. I think the textbook is correct about on the final answer. If $3x+5=3x^2-2x-4$ then $x=5/6\pm 1/6\sqrt{133}$ which is the same as $x\approx -1.089$ or $x\approx 2.755$.
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