Question

Find wheather x²+5√5x-70=0 has real roots.If real roots exists,find them​

Answer 1

Answer:

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Answer 2

x² + 5√5 - 70 = 0

__________ [GIVEN EQUATION]

• We have to find real roots of the above equation.

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Real roots.. means D = 0

• Formula :

D = b² - 4ac.. then

x = $\frac{ - b \: ± \sqrt{D } }{2a}$

OR

x = $\frac{ - b \: ± \sqrt{ {b}^{2} \: - \: 4ac } }{2a}$

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x² + 5√5 - 70 = 0

Here..

a = 1, b = + 5√5 and c = - 70

=> D = (5√5)² - 4(1)(-70)

=> 25(5) + 280

=> 125 + 280

=> 405

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=> x = $\frac{ - (5\sqrt{5}) \: ± \sqrt{405 } }{2(1)}$

=> $\frac{-\:5\sqrt{5}\:±\:9\sqrt{5}}{2}$

• $\frac{-\:5\sqrt{5}\:+\:9\sqrt{5}}{2}$

=> $\frac{4\sqrt{5}}{2}$

=> 2√5

• $\frac{-\:5\sqrt{5}\:-\:9\sqrt{5}}{2}$

=> $\frac{-\:14\sqrt{5}}{2}$

=> - 7√5

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2√5 and - 7√5

____________ [ANSWER]