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

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Answer 1 · 2018-01-29T11:28:02

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]

How do you find the nature of the roots using the discriminant given 4x^2 + x + 5 = 04x^2 + x + 5 = 0?