Question

2/3 and 1 are the solutions of equation mx^2 + nx + 6 = 0. find the values of m and n.​

Answer 1

Answer:

m=(-12), n=6

Step-by-step explanation:

x=⅔,

mx²+nx+6=0

m×(⅔)²+n×⅔+6=0

m×4/9+n×⅔+6=0

4m/9+2n/3+6=0

Multiply each term by 9

4m/9×9+2n/3×9+6=0

4m+6n+6=0

2m+3n+6=0--eq1

x=1

mx²+nx+6=0

m(1)¹+n(1)+6=0

m+n+6=0--eq2

Add eq1 and eq2, we get

m+2n=0

2n=(-m)

n=(-m)/2

Substitute n=(-m)/2 in eq2

m+n+6=0

m-m/2+6=0

(2m-m+12)/2=0

2m-m+12=0

m+12=0

m=(-12)

Substitute m=(-12) in eq 3

n=(-m)/2

n=12/2

n=6