Question

2/3 and 1 are the solution of equation mx2+nx+6=0. find the value of m and n.​

Answer 1

Answer:

m = 9

n = -15

Step-by-step explanation:

We could approach this in a couple of ways.

Method 1

Use the fact that in a quadratic ax²+bx+c, the sum of the roots is -b/a and the product is c/a.  Then in our quadratic mx²+nx+6, we have

6/m = product of roots = (2/3) × 1 = 2/3   =>   m = 6×3/2  => m = 9

-n/m = sum of roots = 2/3 + 1 = 5/3  =>  -n/9 = 5/3  =>  n = -5×9/3  =>  n = -15

6/m

Method 2

We could use the fact that substituting these values for x makes the equation hold.

Putting x = 2/3:

m(2/3)² + n(2/3) + 6 = 0

=>  4m + 6n = -54   [ multiplied through by 9 ]

=>  2m + 3n = -27   [ divided by 2 ]           ... (1)

Putting x = 1:

m(1)² + n(1) + 6 = 0

=> m + n = -6

=> 2m + 2n = -12    [ multiplied by 2 to prepare for the next step ]  ... (2)

Subtracting equation (2) from equation (1):

n = -27 - -12 = -27 + 12 = -15

Putting this into equation (2):

m = -6 - n = -6 - -15 = -6 + 15 = 9

Answer 2

The answer are the following ones :

The Value of m = 9

The value of n = -15