Name: Problem Based on Formation of Quadratic Equation
Uploaded: 2019-07-19
Duration: 5 min 41 s
Description: In this video, we will learn to solve a problem from the chapter Quadratic Equations, where we need to form an equation whose roots are given. Let's watch an...

Question

Determine whether the given values are solutions of the given equation or not:

a^{2} x^{2} - 3 a b x + 2 b^{2} = 0, x = \frac{a}{b}, x = \frac{b}{a}

Accepted Answer

Given equation:

$a^{2} x^{2} - 3 a b x + 2 b^{2} = 0$

Given values of $x$ are $\frac{a}{b}$ and $\frac{b}{a}$ .

The given values of $x$ are the solutions of the given equation if they satisfy the equation.

Substituting $x = \frac{a}{b}$ in the LHS of the given equation, we get:

$a^{2} {(\frac{a}{b})}^{2} - 3 a b (\frac{a}{b}) + 2 b^{2}$

$= \frac{a^{4}}{b^{2}} - 3 a^{2} + 2 b^{2}$

$= \frac{a^{4} - 3 a^{2} b^{2} + 2 b^{4}}{b^{2}} \neq 0$

$∴$ For $x = \frac{a}{b}, a^{2} x^{2} - 3 a b x + 2 b^{2} \neq 0$

Hence, $x = \frac{a}{b}$ is not a solution of the given equation.

Now, substituting $x = \frac{b}{a}$ in the LHS of the given equation, we get:

$a^{2} {(\frac{b}{a})}^{2} - 3 a b (\frac{b}{a}) + 2 b^{2}$

$= a^{2} \times \frac{b^{2}}{a^{2}} - 3 b^{2} + 2 b^{2}$

$= b^{2} - 3 b^{2} + 2 b^{2}$

$= 3 b^{2} - 3 b^{2}$

$= 0$

$=$ RHS

$∴$ For $x = \frac{b}{a}, a^{2} x^{2} - 3 a b x + 2 b^{2} = 0$ .

Hence, $x = \frac{b}{a}$ is a solution of the given equation.

Determine whether the given values are solutions of the given equation or not:
$a^{2} x^{2} - 3 a b x + 2 b^{2} = 0, x = \frac{a}{b}, x = \frac{b}{a}$

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Determine whether the given values are solutions of the given equation or not: a2x2-3abx+2b2=0, x=ab, x=ba

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

Determine whether the given values are solutions of the given equation or not:
$a^{2} x^{2} - 3 a b x + 2 b^{2} = 0, x = \frac{a}{b}, x = \frac{b}{a}$