Answer :
When solving a quadratic equation, several techniques can be employed. Here are the methods you should consider:
1. Solve by taking the square root of both sides (Option A):
- This method is applicable when the quadratic equation can be rearranged to the form [tex]\( ax^2 = c \)[/tex]. You take the square root of both sides to isolate [tex]\( x \)[/tex], leading to [tex]\( x = \pm \sqrt{\frac{c}{a}} \)[/tex].
2. Solve by factoring (Option B):
- This technique involves rewriting the quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] as a product of binomials [tex]\((dx + e)(fx + g) = 0\)[/tex]. You then set each binomial equal to zero and solve for [tex]\(x\)[/tex].
3. Completing the square (likely intended by "forming sums of squares", Option C):
- Completing the square is a method where you transform the quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] into the form [tex]\((x-h)^2 = k\)[/tex]. This makes it easier to solve for [tex]\( x \)[/tex] by taking the square root of both sides.
Therefore, the techniques you have learned so far for solving a quadratic equation are:
- A. Solve by taking the square root of both sides
- B. Solve by factoring
- C. Solve by forming sums of squares
These methods are checked, resulting in the final selection:
☑ A. Solve by taking the square root of both sides
☑ B. Solve by factoring
☑ C. Solve by forming sums of squares
1. Solve by taking the square root of both sides (Option A):
- This method is applicable when the quadratic equation can be rearranged to the form [tex]\( ax^2 = c \)[/tex]. You take the square root of both sides to isolate [tex]\( x \)[/tex], leading to [tex]\( x = \pm \sqrt{\frac{c}{a}} \)[/tex].
2. Solve by factoring (Option B):
- This technique involves rewriting the quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] as a product of binomials [tex]\((dx + e)(fx + g) = 0\)[/tex]. You then set each binomial equal to zero and solve for [tex]\(x\)[/tex].
3. Completing the square (likely intended by "forming sums of squares", Option C):
- Completing the square is a method where you transform the quadratic equation [tex]\( ax^2 + bx + c = 0 \)[/tex] into the form [tex]\((x-h)^2 = k\)[/tex]. This makes it easier to solve for [tex]\( x \)[/tex] by taking the square root of both sides.
Therefore, the techniques you have learned so far for solving a quadratic equation are:
- A. Solve by taking the square root of both sides
- B. Solve by factoring
- C. Solve by forming sums of squares
These methods are checked, resulting in the final selection:
☑ A. Solve by taking the square root of both sides
☑ B. Solve by factoring
☑ C. Solve by forming sums of squares
