Question

if 2 and 3 are zeros of the polynomial 3x square - 2kx+ 2m then find the values of k and m​

Answer 1

Hey Mate..

$3 ({2}^{2} )- 2(2)k + 2m = 0 \\ 12 - 4k + 2m = 0 \\ 6 - 2k + m = 0$

And,

$3( {3}^{2} ) - 6k + 2m = 0 \\ 27 - 6k + 2m = 0$

From eq 1 and 2..

K=7.5

m=9

hope it helped ❤️

Answer 2

Solution :

if 2 and 3 are zeros of the polynomial 3x² - 2kx+ 2m , It's mean Zeroes of this Quadratic Polynomial is 2 and 3 .

Here, Putting Value of x = 2 in Given Quadratic Polynomial.

Quadratic Polynomial : f(x) = 3x² - 2kx+ 2m

f ( 2 ) = 3x² - 2kx+ 2m

⇒ 3(2)² - 2k(2) + 2 m = 0

⇒ 3 (4) - 4k +2m = 0

⇒ 12 - 4k + 2m = 0

⇒ 2m - 4k = - 12 ------(1)

Now, Putting Value of x = 3 in Given Quadratic Polynomial.

Quadratic Polynomial : f(x) = 3x² - 2kx+ 2m

f ( 3 ) = 3x² - 2kx+ 2m = 0

⇒ 3(3)² - 2k(3) + 2m = 0

⇒ 3(9) -6k + 2m = 0

⇒ 27 - 6k + 2m = 0

⇒ 2m - 6k = - 27 -----(2)

Here, Solving Equation 1 and 2 , We Get

2m -4k = -12

2m - 6k = -27

_-__+_____+______

2k = 15

2k = 15 k = 15/2

Now, Putting Value of k in Equation (1),

⇒2m - 4k = -12

⇒ 2m - 4(15/2) = -12

⇒ 2m - 30 = -12

⇒ 2m = -12 + 30

⇒ 2m = 18

⇒ 2m = 18

⇒ m = 18/2

⇒ m = 9

Therefore, Required Value of k and x are 15/2 and 9 respectively.