Question

find the values of m and n for which x=2 and -3 are zeroes of the polynomial 3x2-2mx+2n

Answer 1

GIVEN :

The values x=2 and -3 are zeroes of the polynomial $3x^2-2mx+2n$

TO FIND :

The the values of m and n for which x=2 and -3 are zeroes of the polynomial $3x^2-2mx+2n$

SOLUTION :

Given that the values x=2 and -3 are zeroes of the polynomial $3x^2-2mx+2n$

That is the given polynomial is satisfied for the value  x=2.

Put x=2 in the polynomial $3x^2-2mx+2n$ we get,

$3(2)^2-2m(2)+2n=0$

$3(4)-4m+2n=0$

$12-4m+2n=0$

$-4m+2n=-12\hfill (1)$

Since x=-3 is zero for the given polynomial then it is satisfied for the value  x=-3.

Put x=-3 in the polynomial $3x^2-2mx+2n$ we get,

$3(-3)^2-2m(-3)+2n=0$

$3(9)+6m+2n=0$

$27+6m+2n=0$

$6m+2n=-27\hfill (2)$

Now solving the equations (1) and (2) by subtracting (1) by (2)

-4m+2n=-12

6m+2n=-27

(-)_(-)_(+)____

-10m+0=15

$-m=\frac{15}{10}$

∴ $m=-\frac{3}{2}$

Substitute the value of m in the equation (1) we have,

$-4(-\frac{3}{2})+2n=-12$

$6+2n=-12$

2n=-12-6

$n=-\frac{18}{2}$

∴ n=-9

∴ the value of m and n are $-\frac{3}{2}$ and -9 respectively.

∴ the values are $m=-\frac{3}{2}$ and n=-9 in the given polynomial $3x^2-2mx+2n$

Answer 2

Step-by-step explanation:

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