Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2=12
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Equation 12-x^2=11
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Equation -sin(x)=0
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Equation 4x+5=2x-7
- Express {x} in terms of y where:
- -5*x-6*y=-1
- -17*x-15*y=-17
- -2*x+7*y=-14
- -11*x-1*y=15
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Identical expressions
- a^ two - four *a*x+ four *x^ two - thirty-six = zero
- a squared minus 4 multiply by a multiply by x plus 4 multiply by x squared minus 36 equally 0
- a to the power of two minus four multiply by a multiply by x plus four multiply by x to the power of two minus thirty minus six equally zero
- a2-4*a*x+4*x2-36=0
- a²-4*a*x+4*x²-36=0
- a to the power of 2-4*a*x+4*x to the power of 2-36=0
- a^2-4ax+4x^2-36=0
- a2-4ax+4x2-36=0
- a^2-4*a*x+4*x^2-36=O
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Similar expressions
- a^2-4*a*x+4*x^2+36=0
- a^2+4*a*x+4*x^2-36=0
- a^2-4*a*x-4*x^2-36=0
a^2-4*a*x+4*x^2-36=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:
$$a_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$a_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = - 4 x$$
$$c = 4 x^{2} - 36$$
, then
Because D > 0, then the equation has two roots.
or
$$a_{1} = 2 x + 6$$
Simplify
$$a_{2} = 2 x - 6$$
Simplify
a*a^2 + b*a + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$a_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$a_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = - 4 x$$
$$c = 4 x^{2} - 36$$
, then
D = b^2 - 4 * a * c =
(-4*x)^2 - 4 * (1) * (-36 + 4*x^2) = 144
Because D > 0, then the equation has two roots.
a1 = (-b + sqrt(D)) / (2*a)
a2 = (-b - sqrt(D)) / (2*a)
or
$$a_{1} = 2 x + 6$$
Simplify
$$a_{2} = 2 x - 6$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$a^{2} + a p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - 4 x$$
$$q = \frac{c}{a}$$
$$q = 4 x^{2} - 36$$
Vieta Formulas
$$a_{1} + a_{2} = - p$$
$$a_{1} a_{2} = q$$
$$a_{1} + a_{2} = 4 x$$
$$a_{1} a_{2} = 4 x^{2} - 36$$
$$a^{2} + a p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - 4 x$$
$$q = \frac{c}{a}$$
$$q = 4 x^{2} - 36$$
Vieta Formulas
$$a_{1} + a_{2} = - p$$
$$a_{1} a_{2} = q$$
$$a_{1} + a_{2} = 4 x$$
$$a_{1} a_{2} = 4 x^{2} - 36$$
The graph
Sum and product of roots
[src]
sum
0 + -6 + 2*x + 6 + 2*x
$$\left(2 x + 6\right) + \left(\left(2 x - 6\right) + 0\right)$$
=
4*x
$$4 x$$
product
1*(-6 + 2*x)*(6 + 2*x)
$$1 \cdot \left(2 x - 6\right) \left(2 x + 6\right)$$
=
2 -36 + 4*x
$$4 x^{2} - 36$$
-36 + 4*x^2