Question

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

Answer 1

Answer:

Step-by-step explanation:

2/3 and 1 are the solution or root of the equation:

Standard quadratic equation is = a$x^{2}$ + bx + c:

so the sum of the roots 2/3 + 1 = -b/a and product of the root is = c/a;

Not finding -b/a = 2/3 + 1;

-b/a = 5/3;

By comparing b = -5 and a = 3;

Product of root c/a = 2/3*1 = 2/3;

By comparing we get c = 2 and a = 3;

Putting the value of a, b and c in to standard equation we get:

3$x^{2}$ - 5x + 2 = 0:

Now multiplying 3 both side in the above equation we get

9$x^{2}$ - 15x + 6 = 0: Now comparing this equation with the given equation we get

m = 9 and n = -15

Answer 2

Answer:

2/3 and 1 are the solutions of equation mx²+nx+6=0

Then Value of m = 9 & n = -15

Step-by-step explanation:

2/3 and 1 are the solutions of equation mx²+nx+6=0

2/3 & 1 are roots so

(x - 2/3) (x-1) = 0

=> x² - 2x/3 - x + 2/3= 0

=> 3x² -2x - 3x + 2 = 0

=> 3x² -5x + 2 = 0

multiplying by 3

=> 9x² - 15x + 6 = 0

equating with

mx²+nx+6=0

m = 9

n = -15