Question

For what value of k, the equation \[k{{x}^{2}}-6x-2=0\] has equal roots.

Answer 1

Hint: To find the value of k we will be using the fact that for equal roots, the discriminant value is 0.

Complete step-by-step answer:
As mentioned in the question, we would first require finding the discriminant of the given quadratic equation as follows
\[\begin{align}
  & D={{b}^{2}}-4ac \\
 & D={{\left( -6 \right)}^{2}}-4k(-2) \\
 & D=36+8k \\
\end{align}\]
Now, we have to make D=0 for making the equation have equal roots, so, we get
\[\begin{align}
  & D=0=36+8k \\
 & k=\dfrac{-36}{8} \\
 & k=\dfrac{-9}{2} \\
\end{align}\]
Hence, the required value of k is \[\dfrac{-9}{2}\].

Note: The students can make an error if they don’t know about the discriminant of a quadratic equation which is given as follows-
The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation.
i) A positive discriminant indicates that the quadratic has two distinct real number solutions.
ii) A discriminant of zero indicates that the quadratic has a repeated real number solution.
iii) A negative discriminant indicates that neither of the solutions are real numbers.