Answer :
To determine which of the given numbers are solutions to the quadratic equation [tex]\( x^2 + x - 20 = 0 \)[/tex], we will substitute each option into the equation and see if the left-hand side equals the right-hand side (which is 0).
Let's check each option:
### Option A: [tex]\( x = 4 \)[/tex]
Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[ 4^2 + 4 - 20 = 16 + 4 - 20 = 20 - 20 = 0 \][/tex]
Since the equation holds true for [tex]\( x = 4 \)[/tex], this is a solution.
### Option B: [tex]\( x = -5 \)[/tex]
Substitute [tex]\( x = -5 \)[/tex] into the equation:
[tex]\[ (-5)^2 + (-5) - 20 = 25 - 5 - 20 = 25 - 25 = 0 \][/tex]
Since the equation holds true for [tex]\( x = -5 \)[/tex], this is a solution.
### Option C: [tex]\( x = -20 \)[/tex]
Substitute [tex]\( x = -20 \)[/tex] into the equation:
[tex]\[ (-20)^2 + (-20) - 20 = 400 - 20 - 20 = 400 - 40 = 360 \][/tex]
Since the equation does not hold true for [tex]\( x = -20 \)[/tex], this is not a solution.
### Option D: [tex]\( x = -4 \)[/tex]
Substitute [tex]\( x = -4 \)[/tex] into the equation:
[tex]\[ (-4)^2 + (-4) - 20 = 16 - 4 - 20 = 16 - 24 = -8 \][/tex]
Since the equation does not hold true for [tex]\( x = -4 \)[/tex], this is not a solution.
### Option E: [tex]\( x = 5 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ 5^2 + 5 - 20 = 25 + 5 - 20 = 30 - 20 = 10 \][/tex]
Since the equation does not hold true for [tex]\( x = 5 \)[/tex], this is not a solution.
### Summary
The numbers that satisfy the equation [tex]\( x^2 + x - 20 = 0 \)[/tex] are:
- 4
- -5
Thus, the correct solutions are:
- Option A: 4
- Option B: -5
Let's check each option:
### Option A: [tex]\( x = 4 \)[/tex]
Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[ 4^2 + 4 - 20 = 16 + 4 - 20 = 20 - 20 = 0 \][/tex]
Since the equation holds true for [tex]\( x = 4 \)[/tex], this is a solution.
### Option B: [tex]\( x = -5 \)[/tex]
Substitute [tex]\( x = -5 \)[/tex] into the equation:
[tex]\[ (-5)^2 + (-5) - 20 = 25 - 5 - 20 = 25 - 25 = 0 \][/tex]
Since the equation holds true for [tex]\( x = -5 \)[/tex], this is a solution.
### Option C: [tex]\( x = -20 \)[/tex]
Substitute [tex]\( x = -20 \)[/tex] into the equation:
[tex]\[ (-20)^2 + (-20) - 20 = 400 - 20 - 20 = 400 - 40 = 360 \][/tex]
Since the equation does not hold true for [tex]\( x = -20 \)[/tex], this is not a solution.
### Option D: [tex]\( x = -4 \)[/tex]
Substitute [tex]\( x = -4 \)[/tex] into the equation:
[tex]\[ (-4)^2 + (-4) - 20 = 16 - 4 - 20 = 16 - 24 = -8 \][/tex]
Since the equation does not hold true for [tex]\( x = -4 \)[/tex], this is not a solution.
### Option E: [tex]\( x = 5 \)[/tex]
Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ 5^2 + 5 - 20 = 25 + 5 - 20 = 30 - 20 = 10 \][/tex]
Since the equation does not hold true for [tex]\( x = 5 \)[/tex], this is not a solution.
### Summary
The numbers that satisfy the equation [tex]\( x^2 + x - 20 = 0 \)[/tex] are:
- 4
- -5
Thus, the correct solutions are:
- Option A: 4
- Option B: -5
