Answer:
option (b) is correct.
First step to solve for deriving the quadratic formula from the quadratic equation is completing the square.
Step-by-step explanation:
Given : the quadratic equation [tex]ax^2+bx+c=0[/tex]
We have to find the first step for deriving the quadratic formula from the quadratic equation.
Quadratic formula is given by [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Consider the given quadratic equation [tex]ax^2+bx+c=0[/tex]
Divide the equation by a, we get,
[tex]x^2+\frac{b}{a}x+\frac{c}{a}=0[/tex]
Take [tex]\frac{c}{a}[/tex] to other side, we get,
[tex]x^2+\frac{b}{a}x=-\frac{c}{a}[/tex]
Add [tex](\frac{b}{2a})^2[/tex] to both side, we get,
[tex]x^2+\frac{b}{a}x+(\frac{b}{2a})^2=(\frac{b}{2a})^2-\frac{c}{a}[/tex]
Thus, the left side is in the form of [tex](a+b)^2=a^2+b^2+2ab[/tex]
On solving, we get,
[tex](x+\frac{b}{2a})^2=(\frac{b}{2a})^2-\frac{c}{a}[/tex]
Then solve for x , we get quadratic formula [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Thus, first step to solve for deriving the quadratic formula from the quadratic equation is completing the square.
Thus, option (b) is correct.
