Question

The equation 24x2+25x−47ax−2=−8x−3−53ax−2 is true for all values of x≠2a, where a is a constant.

Answer 1

Answer:

Option B is correct

Explanation:

Value of a is -3

Given the equation:   $\frac{24x^2+25x-47}{ax-2} =-8x-3-\frac{53}{ax-2}$ is true for all $x\neq 2a$

To find the value of a.

Multiply both sides of the given equation by $(ax-2)$, we have;

 $24x^2+25x-47=(-8x-3)(ax-2)-53$

Using FOIL Method to multiply two binomials i.e (-8x-3)(ax-2)

$24x^2+25x-47=-8ax^2+16x-3ax+6-53$

or

$24x^2+25x-47=-8ax^2+x(16-3a)-47$

Since the coefficients of the $x^2$ term have to be equal on both sides of the equation. we have;

-8a = 24

Divide both sides by -8 we get;

a = -3

Therefore, the value of a is, -3