Mister Exam

Other calculators

x^2-9x+20=0

x^2-9x+20=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               
x  - 9*x + 20 = 0
x2−9x+20=0x^{2} - 9 x + 20 = 0
Simplify
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=−9b = -9
c=20c = 20
, then
D = b^2 - 4 * a * c = 

(-9)^2 - 4 * (1) * (20) = 1

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=5x_{1} = 5
Simplify
x2=4x_{2} = 4
Simplify
Vieta's Theorem
it is reduced quadratic equation
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=−9p = -9
q=caq = \frac{c}{a}
q=20q = 20
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=9x_{1} + x_{2} = 9
x1x2=20x_{1} x_{2} = 20
The graph
-7.5-5.0-2.50.02.55.07.522.510.012.515.017.520.0200-100
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 4
x1=4x_{1} = 4
Simplify 
x2 = 5
x2=5x_{2} = 5
Simplify
Sum and product of roots [src] 
sum
0 + 4 + 5
(0+4)+5\left(0 + 4\right) + 5 
=
9
99 
product
1*4*5
1⋅4⋅51 \cdot 4 \cdot 5 
=
20
2020 
20
Numerical answer [src] 
x1 = 4.0
x2 = 5.0
x2 = 5.0
The graph
x^2-9x+20=0 equation
    © Mister Exam – Calculator