## If the roots of the equation are -7/4 , 4/7 then the equation will be?

A. 28x^2+43x-28=0

B. 28x^2-43x-28=0

C. 28x^2+49x-16=0

D. 28x^2-33x-28=0

### Answer

Correct Answer: **C. 28x^2 + 49x -16 = 0 **

### Solution

If the roots of the equation are `-7/4`

and `4/7`

, then the equation can be written as:

(x + 7/4)(x – 4/7) = 0

Multiplying out the terms gives:

x^2 + (7/4)x – (4/7)x – 7/4 * 4/7 = 0

x^2 + (49x – 16)/28 = 0

Multiplying both sides by `28`

to get rid of the denominator, we get:

28x^2 + 49x – 16 = 0

Therefore, the equation with roots `-7/4`

and `4/7`

is `28x^2 + 49x - 16 = 0`

.