Mister Exam

Other calculators

4x^2-9=0

4x^2-9=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        
4*x  - 9 = 0
4x2−9=04 x^{2} - 9 = 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=4a = 4
b=0b = 0
c=−9c = -9
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (4) * (-9) = 144

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

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

or
x1=32x_{1} = \frac{3}{2}
x2=−32x_{2} = - \frac{3}{2}
Vieta's Theorem
rewrite the equation
4x2−9=04 x^{2} - 9 = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−94=0x^{2} - \frac{9}{4} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−94q = - \frac{9}{4}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=−94x_{1} x_{2} = - \frac{9}{4}
The graph
05-15-10-51015-5001000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-3/2 + 3/2
−32+32- \frac{3}{2} + \frac{3}{2} 
=
0
00 
product
-3*3
----
2*2
−94- \frac{9}{4} 
=
-9/4
−94- \frac{9}{4} 
-9/4
Rapid solution [src] 
x1 = -3/2
x1=−32x_{1} = - \frac{3}{2} 
x2 = 3/2
x2=32x_{2} = \frac{3}{2} 
x2 = 3/2
Numerical answer [src] 
x1 = -1.5
x2 = 1.5
x2 = 1.5
The graph
4x^2-9=0 equation
    © Mister Exam – Calculator