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(C) Given equation is $x^{2}+5 \sqrt{5} x-70=0$.On comparing with $ax^{2}+bx+c=0$,we get $a=1, b=5 \sqrt{5}$,and $c=-70$.Discriminant $D = b^{2}-4ac =

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$2 \sqrt{5}, -7 \sqrt{5}$

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(C) Given equation is $x^{2}+5 \sqrt{5} x-70=0$.On comparing with $ax^{2}+bx+c=0$,we get $a=1, b=5 \sqrt{5}$,and $c=-70$.Discriminant $D = b^{2}-4ac = (5 \sqrt{5})^{2}-4(1)(-70) = 125 + 280 = 405$.Since $D > 0$,the equation has two distinct real roots.Using the quadratic formula $x = \frac{-b \pm \sqrt{D}}{2a}$,we get:$x = \frac{-5 \sqrt{5} \pm \sqrt{405}}{2(1)} = \frac{-5 \sqrt{5} \pm 9 \sqrt{5}}{2}$.Case $1$: $x = \frac{-5 \sqrt{5} + 9 \sqrt{5}}{2} = \frac{4 \sqrt{5}}{2} = 2 \sqrt{5}$.Case $2$: $x = \frac{-5 \sqrt{5} - 9 \sqrt{5}}{2} = \frac{-14 \sqrt{5}}{2} = -7 \sqrt{5}$.Thus,the roots are $2 \sqrt{5}$ and $-7 \sqrt{5}$.

Find whether the following equation has real roots. If real roots exist,find them.
$x^{2}+5 \sqrt{5} x-70=0$

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Find whether the following equation has real roots. If real roots exist,find them.$x^{2}+5 \sqrt{5} x-70=0$