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Question
Find whether the following equation have real roots. If real roots exist, find them.
5x2 – 2x – 10 = 0
Solution
Given equation is 5x2 – 2x – 10 = 0
On company with ax2 + bx + c = 0, we get
a = 5, b = – 2 and c = – 10
∴ Discriminant, D = b2 – 4ac
= (–2)2 – 4(5)(–10)
= 4 + 200
= 204 > 0
Therefore, the equation 5x2 – 2x – 10 = 0 has two distinct real roots.
Roots, `x = (-b +- sqrt(D))/(2a)`
= `(-(-2) +- sqrt(204))/(2 xx 5)`
= `(2 +- 2sqrt(51))/10`
= `(1 +- sqrt(51))/5`
= `(1 + sqrt(51))/5, (1 - sqrt(51))/5`
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