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Question
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
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Solution
Given equation is `x^2 + 5sqrt(5)x - 70` = 0
On company with ax2 + bx + c = 0, we get
a = 1, b = `5sqrt(5)` and c = – 70
∴ Discriminant, D = b2 – 4ac
= `(5sqrt(5))^2 - 4(1)(-70)`
= 125 + 280
= 405 > 0
Therefore, the equation `x^2 + 5sqrt(5)x - 70` = 0 has two distinct real roots.
Roots, `x = (-b +- sqrt(D))/(2a)`
= `(-5sqrt(5) +- sqrt(405))/(2(1))`
= `(-5sqrt(5) +- 9sqrt(5))/2`
= `(-5sqrt(5) + 9 sqrt(5))/2, (-5sqrt(5) - 9sqrt(5))/2`
= `(4sqrt(5))/2, - (14 sqrt(5))/2`
= `2sqrt(5), -7sqrt(5)`
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