Check out the image . Question number 5
Pls give me the solution...
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Do you know the "quadratic formula"? What does the quadratic formula give for the two solutions to $\displaystyle x^2+ ax+ b= 0$? What is the difference between them? What does the quadratic formula give for the two solutions to $\displaystyle x^2+ bx+ a= 0$? What is the difference between them? Set those two differences equal. What does that give you?
The roots of $\displaystyle x^2+ax+b=0$ are:
$\displaystyle x=\frac{-a\pm\sqrt{a^2-4b}}{2}$
Taking the difference $\displaystyle \Delta r_1$ to be the larger root minus the smaller, we have:
$\displaystyle \Delta r_1=\sqrt{a^2-4b}$
Likewise, for the second quadratic we would find:
$\displaystyle \Delta r_2=\sqrt{b^2-4a}$
If these differences are the same, this implies:
$\displaystyle a^2-4b=b^2-4a$
Can you proceed?