Part Three 505
Question 22-10
How can we use the quadratic formula to find the roots of the following equation?
−x= 3 x^2 − 4
Answer 22-10
First, let’s get the equation into polynomial standard form. We can do that by adding x to both
sides and then switching the right and left sides. That gives us
3 x^2 +x− 4 = 0
In the general polynomial standard equation
ax^2 +bx+c= 0
we have a= 3, b= 1, and c=−4. Plugging these into the quadratic formula, we get
x= [−b± (b^2 − 4 ac)1/2] / (2a)
= {− 1 ± [1^2 − 4 × 3 × (−4)]1/2} / (2 × 3)
= [− 1 ± (1 + 48)1/2] / 6
= (− 1 ± 49 1/2) / 6
= (− 1 ± 7) / 6
= 6/6 or −8/6
= 1 or −4/3
The roots of the quadratic equation are x= 1 or x=−4/3.
Chapter 23
Question 23-1
Does a quadratic equation with real coefficients and a real constant, but with a negative dis-
criminant, have any roots at all? If so, what are they like?
Answer 23-1
When a quadratic equation with real coefficients and a real constant has a negative discrimi-
nant, the equation has two roots, both of which are non-real complex numbers.
Question 23-2
How can we use the quadratic formula to find the roots of the following equation?
−x= 3 x^2 + 4