Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2=5
-
Equation k^2+k=0
-
Equation 5x=0
-
Equation x^2-15=2x
- Express {x} in terms of y where:
- -4*x+3*y=9
- -2*x-19*y=-11
- -5*x+15*y=-15
- -1*x+7*y=-11
-
Identical expressions
- five *x^ two + nine *x= zero
- 5 multiply by x squared plus 9 multiply by x equally 0
- five multiply by x to the power of two plus nine multiply by x equally zero
- 5*x2+9*x=0
- 5*x²+9*x=0
- 5*x to the power of 2+9*x=0
- 5x^2+9x=0
- 5x2+9x=0
- 5*x^2+9*x=O
-
Similar expressions
- 5*x^2-9*x=0
5*x^2+9*x=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
$$a = 5$$
$$b = 9$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = - \frac{9}{5}$$
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
$$a = 5$$
$$b = 9$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(9)^2 - 4 * (5) * (0) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = - \frac{9}{5}$$
Vieta's Theorem
rewrite the equation
$$5 x^{2} + 9 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{9 x}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{9}{5}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{9}{5}$$
$$x_{1} x_{2} = 0$$
$$5 x^{2} + 9 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{9 x}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{9}{5}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{9}{5}$$
$$x_{1} x_{2} = 0$$
Sum and product of roots
[src]
sum
-9/5
$$- \frac{9}{5}$$
=
-9/5
$$- \frac{9}{5}$$
product
0*(-9) ------ 5
$$\frac{\left(-9\right) 0}{5}$$
=
0
$$0$$
0
The graph