c Make sure you write all the terms on the left-hand side of the equation and simplify as much as possible before using the Quadratic Formula.
A
a 625
B
b Two Real Rational Roots
C
c x=-11 and x= 32
Practice makes perfect
a
In the Quadratic Formula, b^2-4ac is the discriminant.
x=- b±sqrt(b^2-4ac)/2a
Having the equation written in standard form, we can now identify the values of a, b, and c.
2x^2+19x-33=0 ⇔ 2x^2+ 19x+( -33)=0
Let's evaluate the discriminant.
b If we want to know the number of real solutions we only need to work with the discriminant. Remember that if the discriminant is greater than zero, the equation will have two real solutions. If it is equal to zero, the equation will have one real solution. Finally, if the discriminant is less than zero, the equation will have no real solutions. b^2-4ac=625
Since the discriminant is 625, the quadratic equation has two real roots.
ax^2+ bx+ c=0 ⇔ x=- b± sqrt(b^2-4 a c)/2 aWe know that a= 2, b= 19, c= -33, and that the discriminant b^2-4ac=625. Let's substitute these values into the Quadratic Formula.
Using the Quadratic Formula, we found that the solution of the given equation is x= -19 ± 254. Now, we will obtain one of the solutions using the positive sign, and the other one using the negative sign.
ccc
x=-19 + 25/4 & & x=-19 - 25/4
⇓ & & ⇓
x=3/2 & & x=- 11
There are two real solutions, x=-11 and x= 32.
