Question

If x=4 is one root of the quadratic equation x²-2kx-6=0 then find value ok k.​

Answer 1

Answer:

10/8

Step-by-step explanation:

As according to question

p(x) = x²-2kx-6=0

x= 4 is one root of the quadratic equation

Remainder = p(4) = 0

=> p(4)=0

=> (4)²-2k(4) - 6 = 0

=> 16-8k-6=0

=> -8k=6-16

=> - 8k = -10

=> k=10/8

=> k=5/4

Answer 2

Answer :

The value of k is 5/4

and also the other root is -3/2

Given :

The quadratic equation :

• x² - 2kx - 6 = 0
• one root of the equation is 4

To Find :

The value of k

Solution :

Let us consider the other root as β

We know that ,

sum of the roots = -coefficient of x/coefficient of x

⇒ 4 + β = -(-2k)/1

⇒ 4 + β = 2k

⇒ β = 2k - 4 .............(1)

Product of the roots = constant term/coefficient of x²

⇒ 4×β = -6/1

⇒ β = -6/4

⇒β = -3/2 .............(2)

Comparing equation (1) and (2) we have :

2k - 4 = -3/2

⇒ 2k = -3/2 + 4

⇒ 2k = (-3 + 8)/2

⇒ 2k = 5/2

⇒ k = 5/4