Question

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

What is the value of a?

A) -16
B) -3
C) 3
D) 16

Answer 1

Option B is correct

Step-by-step explanation:

Value of a is -3

Given the equation:
`(24x^2+25x-47)/(ax-2) =-8x-3-(53)/(ax-2)` is true for all
`x\\eq 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