Question

algebra 1 sem2
lesson 3.1- solving quadratics by taking square roo
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: Define square root method use

The square root method works for quadratics that can be rewritten as $x^2 = k$ (or $(ax)^2 = k$), meaning no linear $x$-term.

Step2: Analyze each option

• a. $x^2 - 9 = 0$ can be rewritten as $x^2 = 9$ (no linear term, valid)
• b. $8x^2 - 3x + 4 = 0$ has a linear $-3x$ term (invalid)
• c. $x^2 = x + 1$ can be rewritten as $x^2 - x -1=0$ (has linear $-x$ term, invalid)
• d. $4x^2 = 16$ can be rewritten as $x^2 = 4$ (no linear term, valid)
• e. $5x^2 -25 = 0$ can be rewritten as $x^2 = 5$ (no linear term, valid)

Answer:

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