Mister Exam
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How to use it?
- Equation:
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Equation (-5x+3)*(-x+6)=0
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Identical expressions
- x^ two - eleven *x+ ten = zero
- x squared minus 11 multiply by x plus 10 equally 0
- x to the power of two minus eleven multiply by x plus ten equally zero
- x2-11*x+10=0
- x²-11*x+10=0
- x to the power of 2-11*x+10=0
- x^2-11x+10=0
- x2-11x+10=0
- x^2-11*x+10=O
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Similar expressions
- x^2+11*x+10=0
- x^2-11*x-10=0
x^2-11*x+10=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
$$a = 1$$
$$b = -11$$
$$c = 10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 10$$
$$x_{2} = 1$$
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
$$a = 1$$
$$b = -11$$
$$c = 10$$
, then
D = b^2 - 4 * a * c =
(-11)^2 - 4 * (1) * (10) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 10$$
$$x_{2} = 1$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -11$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 11$$
$$x_{1} x_{2} = 10$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -11$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 11$$
$$x_{1} x_{2} = 10$$
The graph