Hacks - Week One Task

Discriminant and Nature of Roots

Our aim is to develop system which finds the discriminant of the quadratic equation and finds its nature.

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Discriminant

The discriminant of a polynomial is a quantity that depends on the coefficients and determines various properties of the roots. The discriminant of a polynomial is generally defined in terms of a polynomial function of its coefficients.

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Nature of Roots

The discriminant determines the nature of the roots of a quadratic equation. The word 'nature' refers to the types of numbers the roots can be — namely real, rational, irrational or imaginary.

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if D>0: "the roots are real and distinct."

if d > 0:
 d**=0.5
 r1 = (-b+d)/(2*a)
 r2 = (-b-d)/(2*a)
 print("The roots are real and distinct")
 print("The roots are :",r1,r2)

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if D=0: "the roots are real and equal."

elif d == 0:
 r = (-b)/(2*a)
 print("The roots are real and equal")
 print("The roots are : {}, {}".format(r,r))

if D<0: "the roots are imaginary."

else:
 d = ((4*a*c)-(b**2))**0.5
 r = (-b)/(2*a)
 i = (d)/(2*a)
 print("Imaginary roots")
 print("The roots are : {}+{}i, {}-{}i".format(r,i,r,i))