Question

Please help me with my son math problem he keeps getting it wrong and we have a chance to redo it. I have included the image of the problem please help

Answer 1

Recall that the discriminant of a quadratic equation:

`ax^2+bx+c=0`

is:

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

We know that:

1) If Δ=0 then the quadratic equation has one double root.

2) If Δ>0 then the quadratic equation has two different real roots.

3) If Δ<0 then the quadratic equation has two different nonreal roots.

Now, we can rewrite the given equation as follows:

`5y^2-18y+4=0.`

The discriminant of the above equation is:

`\Delta=(-18)^2-4(5)(4)\text{.}`

Simplifying the above result we get:

`\begin{gathered} \Delta=324-80 \\ =244. \end{gathered}`

Since:

`\Delta>0.`

Then the given equation has two different real solutions.

Finally, notice that:

`\sqrt[]{244}=2\sqrt[]{61}`

Therefore the solutions are both irrational.

Answer: Last option.