Answer:
x = -1 + (1/2)√6
x = -1 - (1/2)√6
Step-by-step explanation:
To find the roots of the quadratic equation y = 2x^2 + 4x - 1, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Where a = 2, b = 4, and c = -1.
Plugging these values into the quadratic formula, we get:
x = (-4 ± √(4^2 - 4*2*(-1))) / (2*2)
= (-4 ± √(16 + 8)) / 4
= (-4 ± √24) / 4
= (-4 ± 2√6) / 4
= -1 ± (1/2)√6
So the roots of the equation y = 2x^2 + 4x - 1 are:
x = -1 + (1/2)√6
x = -1 - (1/2)√6
Therefore, the roots expressed in the simplest form are:
x = -1 + (1/2)√6
x = -1 - (1/2)√6
