Which of the following are quadratic equations?

$(2x\ +\ 1)(3x\ +\ 2)\ =\ 6(x\ –\ 1)(x\ –\ 2)$

Given:

Given equation is $(2x\ +\ 1)(3x\ +\ 2)\ =\ 6(x\ –\ 1)(x\ –\ 2)$.

To do:

We have to check whether the given equation is quadratic.

Solution:

The standard form of a quadratic equation is $ax^2+bx+c=0$.

$(2x\ +\ 1)(3x\ +\ 2)\ =\ 6(x\ –\ 1)(x\ –\ 2)$

$(2x + 1)(3x + 2) = 6(x – 1)(x – 2)$

$6x^2 + 4x + 3x + 2 = 6x^2 -12x – 6x + 12$

$7x + 2 = -18x + 12$

$25x – 10 = 0$

The equation $25x – 10 = 0$ is not of the form $ax^2+bx+c=0$ as its degree is $1$. 

Therefore, $(2x\ +\ 1)(3x\ +\ 2)\ =\ 6(x\ –\ 1)(x\ –\ 2)$ is not a quadratic equation.

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Updated on: 10-Oct-2022

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