Mister Exam
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How to use it?
- Equation:
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Equation |x|=-1
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Equation tan(x)=7
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Equation 6-3*(x+1)=7-2*x
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Equation x^6+1=0
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Identical expressions
- two x^2+5x- three = zero
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- two x squared plus 5x minus three equally zero
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Similar expressions
- 2x^2+5x+3=0
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2x^2+5x-3=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
$$a = 2$$
$$b = 5$$
$$c = -3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{2}$$
$$x_{2} = -3$$
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
$$a = 2$$
$$b = 5$$
$$c = -3$$
, then
D = b^2 - 4 * a * c =
(5)^2 - 4 * (2) * (-3) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{2}$$
$$x_{2} = -3$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} + 5 x\right) - 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{5 x}{2} - \frac{3}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{5}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{3}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{5}{2}$$
$$x_{1} x_{2} = - \frac{3}{2}$$
$$\left(2 x^{2} + 5 x\right) - 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{5 x}{2} - \frac{3}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{5}{2}$$
$$q = \frac{c}{a}$$
$$q = - \frac{3}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{5}{2}$$
$$x_{1} x_{2} = - \frac{3}{2}$$
Sum and product of roots
[src]
sum
-3 + 1/2
$$-3 + \frac{1}{2}$$
=
-5/2
$$- \frac{5}{2}$$
product
-3 --- 2
$$- \frac{3}{2}$$
=
-3/2
$$- \frac{3}{2}$$
-3/2
The graph