Mister Exam

Other calculators

k^2+4*k+3=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
 2              
k  + 4*k + 3 = 0
(k2+4k)+3=0\left(k^{2} + 4 k\right) + 3 = 0
Simplify
Detail solution
This equation is of the form
a*k^2 + b*k + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
k1=D−b2ak_{1} = \frac{\sqrt{D} - b}{2 a}
k2=−D−b2ak_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=4b = 4
c=3c = 3
, then
D = b^2 - 4 * a * c = 

(4)^2 - 4 * (1) * (3) = 4

Because D > 0, then the equation has two roots.
k1 = (-b + sqrt(D)) / (2*a)

k2 = (-b - sqrt(D)) / (2*a)

or
k1=−1k_{1} = -1
k2=−3k_{2} = -3
Vieta's Theorem
it is reduced quadratic equation
k2+kp+q=0k^{2} + k p + q = 0
where
p=bap = \frac{b}{a}
p=4p = 4
q=caq = \frac{c}{a}
q=3q = 3
Vieta Formulas
k1+k2=−pk_{1} + k_{2} = - p
k1k2=qk_{1} k_{2} = q
k1+k2=−4k_{1} + k_{2} = -4
k1k2=3k_{1} k_{2} = 3
The graph
05-15-10-510200-100
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-3 - 1
−3−1-3 - 1 
=
-4
−4-4 
product
-3*(-1)
−−3- -3 
=
3
33 
3
Rapid solution [src] 
k1 = -3
k1=−3k_{1} = -3 
k2 = -1
k2=−1k_{2} = -1 
k2 = -1
Numerical answer [src] 
k1 = -3.0
k2 = -1.0
k2 = -1.0
    © Mister Exam – Calculator