## A little note : IITJEE foundation maths

Example:

Solve $2(x^{2}-6)=3(x-4)$

Solution:

We have $2x^{2}-12=3x-12$

that is, $2x^{2}=3x$ call this as Equation (1)

Transposing, $2x^{2}-3x=0$

$x(2x-3)=0$

Hence, $x=0$, or $2x-3=0$

Thus, the roots are 0 and $\frac{3}{2}$

Note:

In equation (1), above, we might have divided both sides by x and obtained the simple equation $2x=3$, hence, $x=\frac{3}{2}$, which is one of the solutions of the given equation. But, the student must be particularly careful to notice that whenever an x, or a factor containing x, is removed by division from every term of an equation, it must not be neglected, since the equation is satisfied by $x=0$, which is therefore, one of the roots.

More on IITJEE foundation maths later,

Nalin Pithwa

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