Question

if one root of the equation 3y2 - KY + 8 = 0 is 2/3, then find the value of k.​

Answer 1

Step-by-step explanation:

3y²-ky+8 has root y=2/3 so it means y=2/3 should satisfy the equation. from here you will get k= -10. So your final answer is K= -10.

Answer 2

Given :-

Quadratic equation 3y² - ky + 8=0

One of the root is 2/3

To find:-

Value of k

SOLUTION:-

As they given 2/3 is a root Since , if we substitute in place of y it should be equal to 0 and then we get value of k

So, substitute y = 2/3

$3y {}^{2} - ky + 8 = 0$

$3\bigg(\dfrac{2}{3}\bigg) {}^{2} - k\bigg(\dfrac{2}{3}\bigg) + 8 = 0$

$3\bigg(\dfrac{4}{9}\bigg ) - \dfrac{2k}{3} + 8 = 0$

$\dfrac{4}{3} - \dfrac{2k}{3} + 8 = 0$

Taking L.C.M to the denominators

$\dfrac{4 - 2k + 24}{3} = 0$

$\dfrac{28 - 2k}{3} = 0$

$28 - 2k = 0(3)$

$28 - 2k = 0$

$28 = 2k$

$k = \dfrac{28}{2}$

$k = 14$

So, the value of k is 14

Verification:-

Substitute value of k and y it should be equal to 0

3y²-ky + 8=0

• k = 14
• y = 2/3

3(2/3)² -14(2/3) + 8 =0

3(4/9) -28/3 +8 =0

4/3 -28/3 +8 =0

4-28 +24/3=0

28-28/3=0

0/3 =0

0=0

Hence verified !

LHS = RHS