Question

1. Use the discriminant to determine allvalues of k which would result in theequation (In the photo) having imaginaryroots.

Answer 1

given data:

The given quadratic equation is

`2x^2+8x+k=0`

To find the value of the discriminant and determinte all the values of k that would result in having imaginary root.

The discriminant is a part of the quadratic formula that is under the square root,

`b^2-4ac`

now, from the given quadratic equation,

a= 2, b=8 and c=k.

subsitute the above values in the discriminant formula,

`\begin{gathered} (8)^2-4\cdot2\cdot k \\ 64-8k \end{gathered}`

for the roots to be imaginary the roots should be negative fo that value of k should be greater than 8.

`k>8`