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How do you find the nature of the roots using the discriminant given #4x^2 + x + 5 = 0#?

Answer 1

Genesis Allen

Nature of roots are complex and #x ~~ -0.125+- 1.11i #

# 4x^2+x+5=0#

Comparing with standard quadratic equation #ax^2+bx+c=0#

# a=4 ,b=1 ,c=5# Discriminant # D= b^2-4ac# or

#D=1-80 = -79# If discriminant positive, we get two real

solutions, if it is zero we get just one solution, and if it is negative

we get complex solutions. Here discriminant is negative , so it has

complex roots . Quadratic formula: #x= (-b+-sqrtD)/(2a) #or

#x= (-1+-sqrt (-79))/8 or x=-1/8+- sqrt(79i^2)/8 ; [i^2=-1] #

or #x ~~ -0.125+- 1.11i #

Nature of roots are complex and #x ~~ -0.125+- 1.11i # [Ans]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.