What is relation between a and b in below equations (I and II) -
I. $9a^2+18a+5=0$
II. $2b^2+13b+20=0$
Options -
a. a>b
b. a>=b
c. a<b
d. a<=b
e. a=b or the relationship between a and b can not be established.
Any help is deeply appreciated. Struggling for few hours with it.
$9a^2 + 18a + 5 = 0 \to 9(a+1)^2 = 4$. Thus: $3(a+1) = \pm 2$, and $a+1 = \pm \dfrac{2}{3}$, and $a = - 1 \pm \dfrac{2}{3} = -\dfrac{1}{3}$ or $-\dfrac{5}{3}$.
The other equation gives: $b^2 + \dfrac{13}{2}b + 10 = 0$ or $\left(b+\dfrac{13}{4}\right)^2 = \dfrac{9}{16}$, or $b + \dfrac{13}{4} = \pm \dfrac{3}{4}$, or $b = -\dfrac{13}{4} \pm \dfrac{3}{4} = -4$ or $-\dfrac{5}{2}$. In either cases $a > b$.