Score: \( 59.5 / 100 \) Answered: \( 28 / 40 \) Question 35 Vvaluate: \( b^{2}-4 a c \) where \( a=2, b=-7 \) and \( c=-5 \). Question Help: Video 1 Video 2 D Post to forum Submit Question

To evaluate the expression \( b^{2} - 4ac \) with \( a = 2 \), \( b = -7 \), and \( c = -5 \), first, substitute the values into the equation: \[ (-7)^{2} - 4(2)(-5) \] Calculating \( (-7)^{2} \) gives you \( 49 \), and \( -4(2)(-5) \) simplifies to \( 40 \), leading to the expression \( 49 + 40 = 89 \). Therefore, the evaluation result is \( 89 \). Now, let’s keep in mind that this expression is known as the discriminant in the quadratic formula. It helps determine the nature of the roots of a quadratic equation. If the discriminant is positive, there are two distinct real roots; if it’s zero, there's exactly one real root; and if negative, the roots are complex. It’s like a crystal ball for predicting the type of solutions you will encounter!