a Identify the values a = 1, b = 2, and c = -3, then substitute into the Quadratic Formula.
B
b Identify the values a = 1, b = -4, and c = 4, then substitute into the Quadratic Formula.
C
c Identify the values a = 1, b = 4, and c = 5, then substitute into the Quadratic Formula.
A
a 1 and -3
B
b 2
C
c No real solution.
Practice makes perfect
a For this exercise, we need to identify our values for a, b, and c, then substitute them into the Quadratic Formula. Let's start by identifying the parts of a standard quadratic.
ccc
ax^2&+& bx&+&c &=& 0
↕ & & ↕ & & ↕ & & ↕
1x^2&+& 2x& + & (-3)&=&0Now, let's substitute a= 1, b= 2, and c = -3 into the Quadratic Formula.
The solutions for this equation are x= - 2± 42. Let's separate them into the positive and negative cases.
x=- 2± 4/2
x_1=- 2+4/2
x_2=- 2-4/2
x_1=2/2
x_2=- 6/2
x_1=1
x_2=- 3
Using the Quadratic Formula, we found that the solutions of the given equation are x_1=1 and x_2=- 3.
b For this exercise, we also need to identify our values for a, b, and c, then substitute them into the Quadratic Formula. Let's start by identifying the parts of a standard quadratic.
ccc
ax^2&+& bx&+&c &=& 0
↕ & & ↕ & & ↕ & & ↕
1x^2&+&( -4)x& + & 4&=&0
Now, let's substitute a= 1, b= -4, and c = 4 into the quadratic formula.
c For this exercise, again we need to identify our values for a, b, and c, then substitute them into the Quadratic Formula. Let's start by identifying the parts of a standard quadratic.
ccc
ax^2&+& bx&+&c &=& 0
↕ & & ↕ & & ↕ & & ↕
1x^2&+& 4x& + & 5&=&0
Now, let's substitute a= 1, b= 4, and c = 5 into the quadratic formula.
