Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.