Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4x^2+7=7+24x
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Equation 2*sin(x)/2=1-cos(x)
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Equation k^2+k-2=0
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Equation 2+7x-4x^2=0
- Express {x} in terms of y where:
- 16*x-20*y=-4
- 20*x+4*y=-7
- -1*x-17*y=-12
- -2*x+1*y=-8
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Identical expressions
- two +7x-4x^ two = zero
- 2 plus 7x minus 4x squared equally 0
- two plus 7x minus 4x to the power of two equally zero
- 2+7x-4x2=0
- 2+7x-4x²=0
- 2+7x-4x to the power of 2=0
- 2+7x-4x^2=O
-
Similar expressions
- 2+7x+4x^2=0
- 2-7x-4x^2=0
2+7x-4x^2=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
$$a = -4$$
$$b = 7$$
$$c = 2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{1}{4}$$
$$x_{2} = 2$$
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
$$a = -4$$
$$b = 7$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(7)^2 - 4 * (-4) * (2) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{1}{4}$$
$$x_{2} = 2$$
Vieta's Theorem
rewrite the equation
$$- 4 x^{2} + \left(7 x + 2\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{7 x}{4} - \frac{1}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{7}{4}$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{7}{4}$$
$$x_{1} x_{2} = - \frac{1}{2}$$
$$- 4 x^{2} + \left(7 x + 2\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{7 x}{4} - \frac{1}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{7}{4}$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{7}{4}$$
$$x_{1} x_{2} = - \frac{1}{2}$$
Sum and product of roots
[src]
sum
2 - 1/4
$$- \frac{1}{4} + 2$$
=
7/4
$$\frac{7}{4}$$
product
2*(-1) ------ 4
$$\frac{\left(-1\right) 2}{4}$$
=
-1/2
$$- \frac{1}{2}$$
-1/2
The graph