Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^3=3
-
Equation 5-x^2=0
- Equation (-5*x+3)*(-x+8)=0
-
Equation x^2+6=5x
- Express {x} in terms of y where:
- -6*x+11*y=-5
- -3*x-19*y=-9
- -19*x-15*y=15
- 13*x-11*y=16
- Graphing y =:
- 5x^2+9x+4
-
Identical expressions
- 5x^ two +9x+ four = zero
- 5x squared plus 9x plus 4 equally 0
- 5x to the power of two plus 9x plus four equally zero
- 5x2+9x+4=0
- 5x²+9x+4=0
- 5x to the power of 2+9x+4=0
- 5x^2+9x+4=O
-
Similar expressions
- 5x^2+9x-4=0
- 5x^2-9x+4=0
5x^2+9x+4=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
$$a = 5$$
$$b = 9$$
$$c = 4$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{4}{5}$$
$$x_{2} = -1$$
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
$$a = 5$$
$$b = 9$$
$$c = 4$$
, then
D = b^2 - 4 * a * c =
(9)^2 - 4 * (5) * (4) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{4}{5}$$
$$x_{2} = -1$$
Vieta's Theorem
rewrite the equation
$$\left(5 x^{2} + 9 x\right) + 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{9 x}{5} + \frac{4}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{9}{5}$$
$$q = \frac{c}{a}$$
$$q = \frac{4}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{9}{5}$$
$$x_{1} x_{2} = \frac{4}{5}$$
$$\left(5 x^{2} + 9 x\right) + 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{9 x}{5} + \frac{4}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{9}{5}$$
$$q = \frac{c}{a}$$
$$q = \frac{4}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{9}{5}$$
$$x_{1} x_{2} = \frac{4}{5}$$
Sum and product of roots
[src]
sum
-1 - 4/5
$$-1 - \frac{4}{5}$$
=
-9/5
$$- \frac{9}{5}$$
product
-(-4) ------ 5
$$- \frac{-4}{5}$$
=
4/5
$$\frac{4}{5}$$
4/5
The graph