\[ 6 x^{2}-2 x+7=0 \] Part: \( 0 / 2 \) Part 1 of 2 Discriminant:

To find the discriminant of the quadratic equation \( 6x^{2} - 2x + 7 = 0 \), we can use the formula \( D = b^2 - 4ac \), where \( a = 6 \), \( b = -2 \), and \( c = 7 \). Plugging in the values, we get: \[ D = (-2)^2 - 4(6)(7) = 4 - 168 = -164 \] Since the discriminant is negative (-164), this indicates that the equation has no real solutions, but rather two complex solutions. Now, how exciting is it to explore the world of quadratic equations? They have been a critical development in mathematics for centuries, coming from the ancient Babylonians who were solving for unknowns like variables in a puzzle! Quadratics have applications in various fields, including physics, engineering, and finance, helping us model situations involving anything from projectile motion to maximizing profit.