Question

For what value of the constant $k$ does the quadratic $2x^2 - 5x + k$ have a double root?

Answer 1

2x^2-5x+k has a double root when k= 3.125 or 3 and 1/8.

Answer 2

Answer: The required value of k is
`(25)/(8).`

Step-by-step explanation: We are given to find the value of k for which the following quadratic equation has a double root :

`2x^2-5x+k=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We know that

a quadratic equation
`ax^2+bx+c,~a\\eq 0` has a double root if its discriminant is 0.

That is,

`b^2-4ac=0.`

For the given equation (i), we have

a = 2, b = -5 and c = k

Therefore, the equation (i) will have a double root if

`b^2-4ac=0\\\\\Rightarrow (-5)^2-4*2* k=0\\\\\Rightarrow 25-8k=0\\\\\Rightarrow 8k=25\\\\\Rightarrow k=(25)/(8).`

Thus, the required value of k is
`(25)/(8).`