Quadratic equation calculator

Quadratic equation has the basic form: ax2+bx+c=0
eq2
Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.


Calculation:

a2−3a+1=0 a2−3a+1=0  p=1;q=−3;r=1 D=q2−4pr=32−4⋅1⋅1=5 D>0  a1,2=−q±D2p=3±52 a1,2=1.5±1.118034 a1=2.618033989 a2=0.381966011   Factored form of the equation:  (a−2.618033989)(a−0.381966011)=0 a^2-3a+1=0 \ \\ a^2 -3a +1 =0 \ \\ \ \\ p=1; q=-3; r=1 \ \\ D = q^2 - 4pr = 3^2 - 4 \cdot 1 \cdot 1 = 5 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 3 \pm \sqrt{ 5 } }{ 2 } \ \\ a_{1,2} = 1.5 \pm 1.118034 \ \\ a_{1} = 2.618033989 \ \\ a_{2} = 0.381966011 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -2.618033989) (a -0.381966011) = 0 \ \\

Solution in text:

a2-3a+1=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 5
D > 0 ... The equation has two distinct real roots

a1 = 2.618034
a2 = 0.381966

P = {2.618034; 0.381966}