# find the set of values...?

• Jan 7th 2009, 10:52 AM
RubbishAtMaths
find the set of values...?
Find the set of values of k for which the equation 2x(sqrd) + kx + 2 = 0 has no real roots.

i have no idea how to solve this... can somone please explain?

thanks
• Jan 7th 2009, 10:58 AM
Mush
Quote:

Originally Posted by RubbishAtMaths
Find the set of values of k for which the equation 2x(sqrd) + kx + 2 = 0 has no real roots.

i have no idea how to solve this... can somone please explain?

thanks

A quadratic equation of the form \$\displaystyle ax^2+bc+c = 0 \$ has no real roots when its discriminant (\$\displaystyle b^2-4ac\$) is less than 0.

In other word, you have to find values of k for which:

\$\displaystyle k^2-4(2)(2) < 0\$
• Jan 7th 2009, 11:10 AM
RubbishAtMaths
Quote:

Originally Posted by Mush
A quadratic equation of the form \$\displaystyle ax^2+bc+c = 0 \$ has no real roots when its discriminant (\$\displaystyle b^2-4ac\$) is less than 0.

In other word, you have to find values of k for which:

\$\displaystyle k^2-4(2)(2) < 0\$

\$\displaystyle k^2 < 16\$ so is the answer \$\displaystyle -4 < k < 4\$?
• Jan 7th 2009, 11:15 AM
Mush
Quote:

Originally Posted by RubbishAtMaths
\$\displaystyle k^2 < 16\$ so is the answer \$\displaystyle -4 < k < 4\$?

Yep!