Question

please mention the above answer​

Answer 1

» Given :

p(x) = 4mnx²-6m²x -6n²x+9mn(m,n ≠ 0)

» Solution -

p(x) = 4mnx²-6m²x -6n²x+9mn

= 2mx(2nx -3m)-3n (2nx -3m)

= (2mx -3n)(2nx -3m) = 0

one of the terms should be 0

2mx -3n = 0

2mx = 3n

x = $\frac{3n}{2m}$

2nx -3m = 0

2nx = 3m

$\frac{3m}{2n}\\ \\ \\ x= \frac{3m}{2n}$

${\pink{\boxed{\therefore\:one\:root\:of\:p(x)\:= \frac{3n}{2m}\: (option \:b)}}}$

Answer 2

Answer:

3m / 2n

Step-by-step explanation:

Given,

P(x) = 4mnx²- 6m²x - 6n²x + 9mn , (m,n ≠ 0)

Since, the quadratic equation has like terms. So let us use the method of Splitting the Middle Term.

➡ P(x) = 2mx•(2nx - 3m) - 3n•(2nx - 3m)

➡ 2mx•(2nx - 3m) - 3n•(2nx - 3m) = 0

Now, let us take common the like terms,

➡ (2mx - 3n) • (2nx - 3m) = 0

Here, either, (2mx - 3n) = 0 or (2nx - 3m) = 0.

Then,

For the values of x :

=> CASE I -

(2mx - 3n) = 0

=> 2mx = 3n

=> x = 3n / 2m

=> CASE II -

=> (2nx - 3m) = 0

=> 2nx = 3m

=> x = 3m / 2n

Hence, the values of x = 3n/2m , 3m/2n