Question

pls explain ...........

Answer 1

If a Value is a Solution to an Equation, then it should satisfy the respective Equation.

Suppose if 'z' is a Solution to an Equation [f(x)], then as the value of z satisfies the  Equation [f(x)] ⇒ f(z) should be equal to zero i.e. [f(z) = 0]

Let the Given Quadratic Polynomial : 3x² - 2kx + 2m be p(x)

Given : x = 2 is the solution of the given Quadratic Equation

⇒ p(2) should be equal to zero

⇒ p(2) = 3(2)² - 2k(2) + 2m

⇒ 3(2)² - 2k(2) + 2m = 0

⇒ 3(4) - 4k + 2m = 0

⇒ 4k - 2m = 12 ------------------- [1]

Given : x = 3 is the solution of the given Quadratic Equation

⇒ p(3) should be equal to zero

⇒ p(3) = 3(3)² - 2k(3) + 2m

⇒ 3(3)² - 2k(3) + 2m = 0

⇒ 3(9) - 6k + 2m = 0

⇒ 6k - 2m = 27 --------------------- [2]

Subtracting Equation [1] from Equation [2], We get :

⇒ (6k - 2m) - (4k - 2m) = 27 - 12

⇒ 6k - 2m - 4k + 2m = 15

⇒ 2k = 15

$\mathsf{\implies k = \frac{15}{2}}$

Substituting the value of k in Equation [1], We get :

$\mathsf{\implies 4(\frac{15}{2}) - 2m = 12}$

$\mathsf{\implies 30 - 2m = 12}$

$\mathsf{\implies 2m = 30 - 12}$

$\mathsf{\implies 2m = 18}$

$\mathsf{\implies m = 9}$