Quadratic equation calculator

Quadratic equation has the basic form: ax**2+bx+c=0 ; ;
eq2
Enter the coefficients a, b, c of quadratic equation in its basic standardized form. Solution of quadratic equations are usually two different real or complex roots, or one double root. Calculation is done by using the discriminant.


Calculation:

13**2 = (-3-2)**2+(-5-k)**2 ; ; -k**2 -10k +119 =0 ; ; k**2 +10k -119 =0 ; ; a=1; b=10; c=-119 ; ; D = b**2 - 4ac = 10**2 - 4 * 1 * (-119) = 576 ; ; D>0 ; ; ; ; k_{1,2} = fraction{ -b ± sqrt{ D } }{ 2a } = fraction{ -10 ± sqrt{ 576 } }{ 2 } ; ; k_{1,2} = fraction{ -10 ± 24 }{ 2 } ; ; k_{1,2} = -5 ± 12 ; ; k_{1} = 7 ; ; k_{2} = -17 ; ; ; ; text{ Factored form: } ; ; (k -7) (k +17) = 0 ; ;

Solution in text:

-k2-10k+119=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 576
D>0 ... The equation has two distinct real roots

k1 = 7
k2 = -17

P = {7; -17}