Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4x^2-4x+1=0
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Equation x-4=0
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Equation x^4=1
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Equation 3*x=0
- Express {x} in terms of y where:
- -17*x+16*y=-19
- -1*x-15*y=13
- -11*x+16*y=3
- -1*x+14*y=1
- Graphing y =:
- x^2-15*x+56
-
Identical expressions
- x^ two - fifteen *x+ fifty-six = zero
- x squared minus 15 multiply by x plus 56 equally 0
- x to the power of two minus fifteen multiply by x plus fifty minus six equally zero
- x2-15*x+56=0
- x²-15*x+56=0
- x to the power of 2-15*x+56=0
- x^2-15x+56=0
- x2-15x+56=0
- x^2-15*x+56=O
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Similar expressions
- x^2-15*x-56=0
- x^2+15*x+56=0
x^2-15*x+56=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
$$a = 1$$
$$b = -15$$
$$c = 56$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 8$$
$$x_{2} = 7$$
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
$$a = 1$$
$$b = -15$$
$$c = 56$$
, then
D = b^2 - 4 * a * c =
(-15)^2 - 4 * (1) * (56) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 8$$
$$x_{2} = 7$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -15$$
$$q = \frac{c}{a}$$
$$q = 56$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 15$$
$$x_{1} x_{2} = 56$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -15$$
$$q = \frac{c}{a}$$
$$q = 56$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 15$$
$$x_{1} x_{2} = 56$$
Sum and product of roots
[src]
sum
7 + 8
$$7 + 8$$
=
15
$$15$$
product
7*8
$$7 \cdot 8$$
=
56
$$56$$
56
The graph