Quadratic equation calculator

Quadratic equation has the basic form:
ax2+bx+c=0ax^2+bx+c=0

eq2
Enter the coefficients a, b, c of quadratic equation in 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:

a23a+1=0 a23a+1=0  p=1;q=3;r=1 D=q24pr=32411=5 D>0  a1,2=q±D2p=3±52 a1,2=1.5±1.1180339887499 a1=2.6180339887499 a2=0.38196601125011   Factored form of the equation:  (a2.6180339887499)(a0.38196601125011)=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 1.1180339887499 \ \\ a_{1} = 2.6180339887499 \ \\ a_{2} = 0.38196601125011 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -2.6180339887499) (a -0.38196601125011) = 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 = 2.6180339887499
a2 = 0.38196601125011

P = {2.6180339887499; 0.38196601125011}