Evaluate the discriminant and determine t \[ 4 x^{2}-5 x+7=0 \] Part: \( 0 / 2 \) Part 1 of 2 Discriminant: \( \square \)

To find the discriminant of the quadratic equation \( 4x^{2} - 5x + 7 = 0 \), we use the formula \( D = b^2 - 4ac \), where \( a = 4 \), \( b = -5 \), and \( c = 7 \). Calculating the discriminant: \[ D = (-5)^{2} - 4 \cdot 4 \cdot 7 = 25 - 112 = -87 \] So, the discriminant is \( -87 \). Now, since the discriminant is negative, this means the equation has no real solutions, but two complex solutions. If you're looking for how "t" is determined, it generally refers to the roots which can be found using the quadratic formula: \[ x = \frac{-b \pm \sqrt{D}}{2a} \] Since \(D\) is negative, we have: \[ x = \frac{5 \pm \sqrt{-87}}{8} = \frac{5 \pm i\sqrt{87}}{8} \] So, t can represent either of these complex roots!