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:

a(a+1)=1+(a+(a+1)) a2a2=0  p=1;q=1;r=2 D=q24pr=1241(2)=9 D>0  a1,2=q±D2p=1±92 a1,2=1±32 a1,2=0.5±1.5 a1=2 a2=1   Factored form of the equation:  (a2)(a+1)=0 a*(a+1) = 1+ (a + (a+1)) \ \\ a^2 -a -2 =0 \ \\ \ \\ p=1; q=-1; r=-2 \ \\ D = q^2 - 4pr = 1^2 - 4\cdot 1 \cdot (-2) = 9 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 1 \pm \sqrt{ 9 } }{ 2 } \ \\ a_{1,2} = \dfrac{ 1 \pm 3 }{ 2 } \ \\ a_{1,2} = 0.5 \pm 1.5 \ \\ a_{1} = 2 \ \\ a_{2} = -1 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -2) (a +1) = 0 \ \\

Solution in text:

a2-a-2=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 9
D>0 ... The equation has two distinct real roots

a1 = 2
a2 = -1

P = {2; -1}