The roots of the equation $x^2 + 18x - 703 = 0$ are given as $a$ and $b$, with $a > b$. The roots of the equation $x^2 - 10x - 336 = 0$ are given as $c$ and $d$, with $c > d$. Which of the options below gives the correct relation between $a$, $b$, $c$, and $d$?

$x^2 + 18x - 703 = 0$

Using $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:

$x = \dfrac{-18 \pm \sqrt{324 + 2812}}{2}$

$= \dfrac{-18 \pm \sqrt{3136}}{2}$

$= \dfrac{-18 \pm 56}{2}$

$x = 19$ or $x = -37$

So $a = 19$, $b = -37$

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$x^2 - 10x - 336 = 0$

Two numbers with product $-336$ and sum $-10$ are $-24$ and $14$:

$(x - 24)(x + 14) = 0$

$x = 24$ or $x = -14$

So $c = 24$, $d = -14$

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Arranging from largest to smallest:

$24 > 19 > -14 > -37$

Therefore, $c > a > d > b$.