Question

If x = 2 and x = 3 are the roots of the equation 3x 2 – 2mx + 2n = 0, find the values of m and n.

Answer 1

f(2)=3×4-4m+2n
0=12-4m+2n
-4m+2n=-12....... eq (1)
f(3)=27-6m+2n=0
-6m+2n=-27....... eq (2)

eq(1)-(2)
2m=15
m=15/2
put m=15/2 in eq (1)
-4×15/2+2n=-12
-30+2n=-12
2n=18
n=9
m=15/2: n=9
is your answer

Answer 2

Answer:

m = -5/2 and n = 1

Step-by-step explanation:

Given:- x = 3 and x = 2 are the roots of the equation $3x^{2} -2mx+2n$

To Find:- Values of m and n in the given equation.

Solution:-

The given equation $3x^{2} -2mx+2n$ is a quadratic equation as it is of degree 2.

Since 2 and 3 are roots of the given polynomial, so we can say that

-2m = 2 + 3

⇒ m = -5/2

We can also say that

3 × 2n = 2 × 3

⇒ 2n = 2

⇒ n = 1.

Putting the value m = -5/2 and n = 1 in the given polynomial, we get

$3x^{2} -2(\frac{-5}{2} )x+2(1)$

= $3x^{2}$ + 5x + 2

Therefore, the value of m is -5/2 and n is 1.

The polynomial whose roots are 2 and 3 is  $3x^{2}$ + 5x + 2.

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