Quadratic equations using the quadratic formula calculator

SolutionHelp

1. Roots of quadratic equation

1. Solving quadratic equations by factoring
2. Solving quadratic equations using the quadratic formula
3. Discriminant
4. Discriminant & nature of roots

Here

$x^2$ = x^2 = x2 and 2x = 2*x

$25x^2 - 30x + 9 = 0$

$2x^2 + 5x - 10 = 0$

$x^2 + 10x - 56 = 0$

$4x^2 + 11x + 10 = 0$

$x^2 - 2x = 8$

$x^2 - 25 = 0$

$x^2 + 5x + 3 = 0$

$9x^2 - 24x + 16 = 0$

2. Find the quadratic equation whose roots are alpha and beta

Input Roots of the Quadratic Equation Like ...

$alpha=3, beta=-4$

$alpha=-1/2, beta=+2/3$

$alpha=2, beta=-2/3$

$alpha=3sqrt(7), beta=-3sqrt(7)$

$alpha=sqrt(7), beta=-sqrt(7)$

$alpha=1+3sqrt(2), beta=1-3sqrt(2)$

$alpha=(3+5sqrt(3))/2, beta=(3-5sqrt(3))/2$

$alpha=(-3+5sqrt(3))/2, beta=(-3-5sqrt(3))/2$

$alpha=(-3+sqrt(3))/2, beta=(-3-sqrt(3))/2$

Example

1. Find the roots of Quadratic Equation $x^2+10x-56=0$ by the method of perfect square

Solution:

$x^2+10x-56=0$

$=>x^2+10x-56 = 0$

Comparing the given equation with the standard quadratic equation

$ax^2+bx+c=0,$

we get,

$a=1, b=10, c=-56.$

$:. Delta=b^2-4ac$

$=(10)^2-4 (1) (-56)$

$=100+224$

$=324$

$:. sqrt(Delta)=sqrt(324)=18$

Now,

$alpha=(-b+sqrt(Delta))/(2a)$

$=(-(10)+18)/(2*1)$

$=8/2$

$=4$

and,

$beta=(-b-sqrt(Delta))/(2a)$

$=(-(10)-18)/(2*1)$

$=-28/2$

$=-14$