Question

Find the type and number of roots of the following equations using the discriminat

Answer 1

Recall that the discriminant of a quadratic equation:

`ax^2+bx+c=0`

is:

`\Delta=b^2-4ac\text{.}`

Also, if:

`\begin{cases}\Delta>0\text{ the quadratic equation has 2 different real roots,} \\ \Delta=0\text{ the quadratic equation has 1 root of }multiplicity\text{ 2,} \\ \Delta<0\text{ the quadratic equation has 2 different imaginary roots.}\end{cases}`

Now, notice that the discriminant of the given equation is:

`\Delta=4^2-4\cdot1\cdot(-2)\text{.}`

Simplifying the above result we get:

`\Delta=16+8=24.`

Since 24>0, we get that the given equation has 2 different real roots.

Answer: The given equation has 2 different real roots.