Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x/4+13=x+1
-
Equation 4(x-8)=-5
-
Equation 5(x-2)^2=-6x-44
-
Equation 2^x=5
- Express {x} in terms of y where:
- 4*x+8*y=7
- -14*x+5*y=3
- 13*x-18*y=-17
- 4*x+18*y=-7
-
Identical expressions
- 4x^ two - nine = zero
- 4x squared minus 9 equally 0
- 4x to the power of two minus nine equally zero
- 4x2-9=0
- 4x²-9=0
- 4x to the power of 2-9=0
- 4x^2-9=O
-
Similar expressions
- 4x^2+9=0
4x^2-9=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 4$$
$$b = 0$$
$$c = -9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{3}{2}$$
$$x_{2} = - \frac{3}{2}$$
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 4$$
$$b = 0$$
$$c = -9$$
, 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
$$x_{1} = \frac{3}{2}$$
$$x_{2} = - \frac{3}{2}$$
Vieta's Theorem
rewrite the equation
$$4 x^{2} - 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{9}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{9}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{9}{4}$$
$$4 x^{2} - 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{9}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{9}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{9}{4}$$
Sum and product of roots
[src]
sum
-3/2 + 3/2
$$- \frac{3}{2} + \frac{3}{2}$$
=
0
$$0$$
product
-3*3 ---- 2*2
$$- \frac{9}{4}$$
=
-9/4
$$- \frac{9}{4}$$
-9/4
The graph