Question

Find the x-intercepts of y = 3x2 + 8x – 1 using the quadratic formula. Express as exact answers.

Answer 1

To find the x-intercepts of the quadratic function y = 3x^2 + 8x - 1, we need to find the values of x when y = 0.

Putting y = 0 in the equation, we get:
0 = 3x^2 + 8x - 1

Using the quadratic formula, x = (-b ± √(b^2 - 4ac))/(2a), where a = 3, b = 8, and c = -1.

Plugging in these values into the quadratic formula, we have:
x = (-8 ± √(8^2 - 4(3)(-1)))/(2(3))
x = (-8 ± √(64 + 12))/6
x = (-8 ± √(76))/6
x = (-8 ± √(4*19))/6
x = (-8 ± 2√19)/6

Simplifying, we have:
x = (-4 ± √19)/3

So, the x-intercepts of the given quadratic function are (-4 + √19)/3 and (-4 - √19)/3.