Name: Solving Free Fall Problem Using Quadratic Equation
Uploaded: 2019-07-19
Duration: 7 min 7 s
Description: In this video, we will learn how we can solve the problem of free fall effectively using the quadratic equation. Let's watch the video and learn.

Question

Solve the given questions by both the methods, first by method of completing the squares, and then by using quadratic formula:

a^{2} x^{2} + 4 a b x + 4 b^{2} = 0

Accepted Answer

Solution of the given quadratic equation by method of completing the squares:

We have,

$a^{2} x^{2} + 4 a b x + 4 b^{2} = 0 \Rightarrow x^{2} + \frac{4 a b}{a^{2}} x + \frac{4 b^{2}}{a^{2}} = 0 \Rightarrow x^{2} + \frac{4 b}{a} x + \frac{4 b^{2}}{a^{2}} = 0 \Rightarrow {(x)}^{2} + 2 \times \frac{2 b}{a} \times x + {(\frac{2 b}{a})}^{2} = 0 \Rightarrow {(x + \frac{2 b}{a})}^{2} = 0 \Rightarrow (x + \frac{2 b}{a}) (x + \frac{2 b}{a}) = 0 \Rightarrow x + \frac{2 b}{a} = 0 or x + \frac{2 b}{a} = 0 \Rightarrow x = - \frac{2 b}{a} o r x = - \frac{2 b}{a}$

Therefore, the required solution is $- \frac{2 b}{a}, - \frac{2 b}{a}$ .

Now, solution of the given quadratic equation by method of quadratic formula:

Comparing the equation $a^{2} x^{2} + 4 a b x + 4 b^{2} = 0$ with $A x^{2} + B x + C = 0, (A \neq 0)$ , we get,

$A = a^{2}, B = 4 a b, C = 4 b^{2} .$

Now, we know,

$x = \frac{- B \pm \sqrt{B^{2} - 4 A C}}{2 A}$

$\Rightarrow x = \frac{- 4 a b \pm \sqrt{{(4 a b)}^{2} - 4 \times a^{2} \times 4 b^{2}}}{2 \times a^{2}} \Rightarrow x = \frac{- 4 a b \pm \sqrt{16 a^{2} b^{2} - 16 a^{2} b^{2}}}{2 a^{2}} \Rightarrow x = \frac{- 4 a b \pm 0}{2 a^{2}} \Rightarrow x = \frac{- 4 a b + 0}{2 a^{2}} or x = \frac{- 4 a b - 0}{2 a^{2}} \Rightarrow x = \frac{- 4 a b}{2 a^{2}} or x = \frac{- 4 a b}{2 a^{2}} \Rightarrow x = - \frac{2 b}{a} or x = - \frac{2 b}{a}$

Therefore, the required solution is $- \frac{2 b}{a}, - \frac{2 b}{a} .$

Solve the given questions by both the methods, first by method of completing the squares, and then by using quadratic formula:
$a^{2} x^{2} + 4 a b x + 4 b^{2} = 0$

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Solve the given questions by both the methods, first by method of completing the squares, and then by using quadratic formula: a2x2+4abx+4b2=0

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Solve the given questions by both the methods, first by method of completing the squares, and then by using quadratic formula:
$a^{2} x^{2} + 4 a b x + 4 b^{2} = 0$