Answer :
Final answer:
The discriminant (∆) of the quadratic equation 2x² - 6 = x, when rearranged to 2x² - x - 6 = 0, is 49, which indicates that the equation has two distinct real solutions.
Explanation:
The question asked involves finding the discriminant (∆) of the quadratic equation 2x² - 6 = x. First, we rearrange the equation to standard form ax² + bx + c = 0, which gives us 2x² - x - 6 = 0. The formula for the discriminant is ∆ = b² - 4ac. Therefore, substituting the values from our equation where a = 2, b = -1, and c = -6, we get ∆ = (-1)² - 4(2)(-6) = 1 + 48 = 49.
This means the discriminant of the quadratic equation 2x² - x - 6 = 0 is 49, indicating that it has two distinct real roots.
