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 $\dfrac{25}{8}.$

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 $ax^2+bx+c,~a\neq 0$ 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

$b^2-4ac=0\\\\\Rightarrow (-5)^2-4\times2\times k=0\\\\\Rightarrow 25-8k=0\\\\\Rightarrow 8k=25\\\\\Rightarrow k=\dfrac{25}{8}.$

Thus, the required value of k is $\dfrac{25}{8}.$