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.