Question

Question 5 of 10

What is the first step in solving a quadratic equation of the form given below?
(ax+ b)² = c
O A. Divide both sides by c
OB. Factor out a common factor
OC. Use the zero product rule
OD. Take the square root of both sides

Answer 1

D

Explanation:

(ax + b)² = c

step 1 : take square root of both sides

ax + b = ±
`√(c)`

step 2 : subtract b from both sides

ax = - b ±
`√(c)`

step 3 : divide both sides by a

x = -
`(b)/(a)` ±
`(√(c) )/(a)`

Answer 2

D. Take the square root of both sides

Explanation:

Given quadratic equation:

`(ax+b)^2=c`

To solve, square root both sides:

`\implies √((ax+b)^2)=√(c)`

`\textsf{Apply radical rule} \quad √(n^2)=n, \quad \textsf{assuming }n \geq 0:`

`\implies ax+b=\pm√(c)`

Subtract b from both sides:

`\implies ax=-b\pm√(c)`

Divide both sides by a:

`\implies x=(-b\pm√(c))/(a), \quad a\\eq 0`