Question

if -2 is a root of the equation 3 x square - 5 x + 2 k = 0. find the value of k​

Answer 1

Answer :

k = -11

Step-by-step explanation :

Given :

-2 is a root of the equation 3x² - 5x + 2k = 0

To find :

the value of k

Solution :

Let p(x) = 3x² - 5x + 2k = 0

Since -2 is a root of the given quadratic equation 3x² - 5x + 2k = 0 , when we substitute x = -2 the result is zero.

i.e., p(-2) = 0

Put x = -2,

3(-2)² - 5(-2) + 2k = 0

3(4) + 10 + 2k = 0

 12 + 10 + 2k = 0

   22 + 2k = 0

    2k = -22

     k = -22/2

     k = -11

The value of k is -11

Verification :

3x² - 5x + 2(-11) = 0

3x² - 5x - 22 = 0

Put x = -2 and check if the result is zero.

 3(-2)² - 5(-2) - 22 = 0

 3(4) + 10 - 22 = 0

 12 + 10 - 22 = 0

  22 - 22 = 0

     0 = 0

 LHS = RHS

Hence verified!

Answer 2

$\huge\sf\underline\red{Solution}$

3x² - 5x + 2k = 0

Given that -2 is a root of equation Hence it is a zero for the the equation

So,substuite value of -2 in given equation as a result we can get value of k

3x² - 5x + 2k = 0

3 (-2)² - 5(-2) + 2k = 0

12 + 10 +2k = 0

22 + 2k = 0

2k = -22

k = -11

VERIFICATION:-

If we put the value of k in equation It should be equal to zero

3x² -5x + 2k = 0

3(-2)² - 5 (-2) + 2(-11) = 0

12 + 10 -22 =0

22 -22 =0

0 =0

Hence value of k is -11