Question
Select all the solutions to the quadratic equation x ^ 2 - 8x - 20 = 0 Select all that apply.
A) x = 4 and x = 5
B) x = - 10 and x = 2
C) x = 10 and x = - 2
D) x = - 4 and x = - 5
A) x = 4 and x = 5
B) x = - 10 and x = 2
C) x = 10 and x = - 2
D) x = - 4 and x = - 5
Answers
GPT-4o mini
To find the solutions to the quadratic equation \( x^2 - 8x - 20 = 0 \), we can either factor the equation or use the quadratic formula.
First, let's try to factor it. We want two numbers that multiply to \(-20\) (the constant term) and add up to \(-8\) (the coefficient of \(x\)). The numbers \(-10\) and \(2\) satisfy these conditions because:
\(-10 \times 2 = -20\)
\(-10 + 2 = -8\)
So, we can write the quadratic equation as:
\((x - 10)(x + 2) = 0\)
Now, setting each factor to zero gives us the solutions:
1. \(x - 10 = 0 \Rightarrow x = 10\)
2. \(x + 2 = 0 \Rightarrow x = -2\)
Thus, the solutions to the quadratic equation \( x^2 - 8x - 20 = 0 \) are \( x = 10 \) and \( x = -2 \).
From the given options, the correct answer is:
C) x = 10 and x = -2
First, let's try to factor it. We want two numbers that multiply to \(-20\) (the constant term) and add up to \(-8\) (the coefficient of \(x\)). The numbers \(-10\) and \(2\) satisfy these conditions because:
\(-10 \times 2 = -20\)
\(-10 + 2 = -8\)
So, we can write the quadratic equation as:
\((x - 10)(x + 2) = 0\)
Now, setting each factor to zero gives us the solutions:
1. \(x - 10 = 0 \Rightarrow x = 10\)
2. \(x + 2 = 0 \Rightarrow x = -2\)
Thus, the solutions to the quadratic equation \( x^2 - 8x - 20 = 0 \) are \( x = 10 \) and \( x = -2 \).
From the given options, the correct answer is:
C) x = 10 and x = -2