b We want to use the discriminant of the given quadratic equation to determine the number and type of the roots. If we do not want to know the exact values of the roots, we only need to work with the discriminant. From Part A, we know that the discriminant of the given equation is 160.
Equation:& 4x-3=- 12x^2
Discriminant:& 160
Since the discriminant is greater than zero and not a perfect square, the quadratic equation has two irrational roots.
c We will use the Quadratic Formula to find the exact solutions of the given equation.
x=- b±sqrt(b^2-4 a c)/2 aRecall that we have already identified the values of a, b, and c in Part A, as well as the discriminant, b^2-4ac.
a= 12, b= 4, c= - 3
Discriminant: 160
Let's substitute these values into the Quadratic Formula.
