Question

one root of 2x² - 5x + k = 0 is twice the other.Find the value of k​

Answer 1

Answer:

Let two roots be a and b of f(x) = 2x²-5x+k

= 0

Alq a=25

Sum of roots = a + b = 2b + b 3b =-5)/2

= 5/2 - b= 5/6

Products of roots = ab = k/2 - 2b.b= 2b² = 2 (5/6)? = 2 x 25/36 = 25/18 = k/2

k = 25/9

Hope my answer is useful

please follow me

Answer 2

ANSWER

Let α be one root of the given equation 2x

2

−5x+k=0. Then the other root of the equation will be 2α.

Then from the relation between the roots and co-efficient we get,

α+2α=

2

5

or, α=

6

5

.....(1) and 2α

2

=

2

k

or α

2

=

4

k

....(2).

Now putting the value of (1) in (2) we get,

36

25

=

4

k

or, k=

9

25

.