Determine the nature of the roots of the following quadratic equations:
$9a^2b^2x^2-24abcdx+16c^2d^2=0, a≠0, b≠0$

Given:

Given quadratic equation is $9a^2b^2x^2-24abcdx+16c^2d^2=0, a≠0, b≠0$.

To do:

We have to determine the nature of the roots of the given quadratic equation.

Solution:

$9a^2b^2x^2-24abcdx+16c^2d^2=0$

Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,

$a=9a^2b^2, b=-24abcd$ and $c=16c^2d^2$.

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.

$D=(-24abcd)^2-4(9a^2b^2)(16c^2d^2)$

$D=576(abcd)^2-576(abcd)^2$

$D=0$

Therefore, the roots of the given quadratic equation are real and equal.

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Updated on: 10-Oct-2022

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