Question

if 2x^2+15x+k=0 had 1/2 as one of its soluutions, what is the value of k?

Answer 1

has*

Answer 2

The quadratic is:

\[\underbrace{2}_A x^2 + \underbrace{15}_B x + \underbrace{k}_C = 0 \]

Consider the number of values that satisfy the equation for different ks with the discriminant:

\[B^2 - 4AC > 0 \implies 2 roots \]
\[B^2 - 4AC = 0 \implies 1 root \]
\[B^2 - 4AC < 0 \implies 0 roots \]

Answer 3

so what do i do now?

Answer 4

2 roots => 15^2 > 8k -> find the range of k.
1 root => 15^2 = 8k -> k = (1 value)