Question

If 2 is the root of the equation 2x^2-(k+1)x+(5k-3) =0, then find the value of k.​

Answer 1

Answer:

k = -1

Explanation:

$f(x) = 2x ^{2} - (k + 1)x + (5k - 3)$

$f(2) = 2(2) ^{2} - (k + 1)2 + (5k - 3) = 0$

$8 - 2k - 2 + 5k - 3 = 0 \\ 8 - 5 - 2k + 5k = 0 \\ 3 + 3k = 0 \\ 3k = - 3 \\ k = - 3 \div 3 \\ k = - 1$

Answer 2

Given:

The root of the equation 2x²-(k+1)x+(5k-3)=0 is 2.

To find:

The value of k

Solution:

The value of k is -1.

We can find the value by following the steps given below-

We know that the root of an equation is the value of the variable which satisfies the equation.

Here, 2 is the root.

So, on substituting the variable x as 2, we should get 0 as the value of the equation.

The equation: 2x²-(k+1)x+(5k-3)=0

Value of x=2

On putting the value of x, we get

2(2)²-(k+1)×2+(5k-3)=0

2×4-2(k+1)+(5k-3)=0

8-2(k+1)+(5k-3)=0

From this equation, we can find the value of k.

Solving the equation,

8-2k-2+5k-3=0

8-2-3-2k+5k=0

3+3k=0

3k= -3

k= -1

Therefore, the value of k is -1.