Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 9^x-8*3^x-9=0
- Equation x+y=4
-
Equation x^2=-3
-
Equation x^2+x+10=0
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- -7*x-13*y=-12
- Derivative of:
- 4x^2+12x+9
-
Identical expressions
- 4x^ two +12x+ nine = zero
- 4x squared plus 12x plus 9 equally 0
- 4x to the power of two plus 12x plus nine equally zero
- 4x2+12x+9=0
- 4x²+12x+9=0
- 4x to the power of 2+12x+9=0
- 4x^2+12x+9=O
-
Similar expressions
- 4x^2+12x-9=0
- 4x^2-12x+9=0
4x^2+12x+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
$$a = 4$$
$$b = 12$$
$$c = 9$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = - \frac{3}{2}$$
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
$$a = 4$$
$$b = 12$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(12)^2 - 4 * (4) * (9) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -12/2/(4)
$$x_{1} = - \frac{3}{2}$$
Vieta's Theorem
rewrite the equation
$$\left(4 x^{2} + 12 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 3 x + \frac{9}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = \frac{9}{4}$$
$$\left(4 x^{2} + 12 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 3 x + \frac{9}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 3$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -3$$
$$x_{1} x_{2} = \frac{9}{4}$$
Sum and product of roots
[src]
sum
-3/2
$$- \frac{3}{2}$$
=
-3/2
$$- \frac{3}{2}$$
product
-3/2
$$- \frac{3}{2}$$
=
-3/2
$$- \frac{3}{2}$$
-3/2
The graph