Final answer:
To find the points of intersection, set the two equations equal to each other and solve for x using the quadratic formula. The points of intersection are (6 + √612)/8 and (6 - √612)/8.
Step-by-step explanation:
To find the points of intersection of the equations 2x² - 5x - 6 and -2x² + x + 30, we can set the two equations equal to each other and solve for x:
2x² - 5x - 6 = -2x² + x + 30
Combining like terms:
4x² - 6x - 36 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values a = 4, b = -6, and c = -36:
x = (-(-6) ± √((-6)² - 4(4)(-36))) / (2(4))
Calculating the discriminant:
x = (6 ± √(36 + 576)) / 8
Simplifying further:
x = (6 ± √612) / 8
Therefore, the two points of intersection of the two equations are (6 + √612)/8 and (6 - √612)/8.