Question

which quadratic equations can be solved using the square root method?
mark all correct answers
a. $x^2 - 9 = 0$
b. $8x^2 - 3x + 4 = 0$
c. $x^2 = x + 1$
d. $4x^2 = 16$
e. $5x^2 - 25 = 0$

Explanation:

Step1: Identify square root method criteria

Quadratic equations in the form $x^2 = k$ (or can be rewritten to this form, no linear $x$ term) are solvable with the square root method.

Step2: Analyze option a

Rewrite to isolate $x^2$:
$x^2 = 9$
This fits the required form.

Step3: Analyze option b

Equation has a linear $-3x$ term, cannot be rewritten as $x^2 = k$. Does not fit.

Step4: Analyze option c

Rearrange to $x^2 - x - 1 = 0$, has a linear $-x$ term. Does not fit.

Step5: Analyze option d

Divide both sides by 4 to isolate $x^2$:
$x^2 = \frac{16}{4} = 4$
This fits the required form.

Step6: Analyze option e

Rewrite to isolate $x^2$:
$5x^2 = 25 \implies x^2 = 5$
This fits the required form.

Answer:

a. $x^2 - 9 = 0$
d. $4x^2 = 16$
e. $5x^2 - 25 = 0$