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Question
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Solution
The given quadratic equation is
x2 + 5x + 5 = 0
Here, a = 1, b = 5 and c = 5
Discriminant
= b2 - 4ac
= (5)2 - 4 x 1 x 5
= 25 - 20
= 5 > 0
so the given equation has real roots given by
a = `(-b + sqrt(b^2 - 4ac))/(2a)`
= `(-5 + sqrt(25 - 4 xx 1 xx 5))/(2 xx 1)`
= `(-5 + sqrt(5))/(2)`
and β = `(-b - sqrt(b^2 - 4ac))/(2a)`
= `(-5 -sqrt(25 - 4 xx 1 xx 5))/(2 xx 1)`
= `(-5 - sqrt(5))/(2)`
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