A Single Solution

As simple as that. We just have to equal the discriminant to 0 as it is asking for 1 real solution. That's it .....BINGO!!! Beta square is 144. So beta is +12 or -12.so answer is 12 as it is only positive

We know that the formula for calculating roots of a quadratic equation $ax^2$ + $bx$ +c = $\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

In this equation ( $b^2-4ac$ ) is called the discriminant .

(1) If $b^2-4ac$ > 0 then the quadratic equation has 2 distinct real solutions.

(2) If $b^2-4ac$ = 0 then the quadratic equation has 1 real solution.

(3) If $b^2-4ac$ < 0 then the quadratic equation has no real solutions.

So, we use the information given in (2) to find out the value of $\beta$

Here $b^2-4ac$ = $\beta^2-(4*4*9)$ = 0

$\beta^2$ = $4*4*9$ = 144

$\beta$ = $\sqrt{144}$ = $\pm 12$

But we only need the positive integral solution which is why the answer is +12