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- Equation:
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Equation x^2-9x+20=0
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Equation (x-2)^2+(x-8)^2=2x^2
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Identical expressions
- x^ two -9x+ twenty = zero
- x squared minus 9x plus 20 equally 0
- x to the power of two minus 9x plus twenty equally zero
- x2-9x+20=0
- x²-9x+20=0
- x to the power of 2-9x+20=0
- x^2-9x+20=O
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Similar expressions
- x^2+9x+20=0
- x^2-9x-20=0
x^2-9x+20=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
$$a = 1$$
$$b = -9$$
$$c = 20$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
Simplify
$$x_{2} = 4$$
Simplify
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
$$a = 1$$
$$b = -9$$
$$c = 20$$
, then
D = b^2 - 4 * a * c =
(-9)^2 - 4 * (1) * (20) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
Simplify
$$x_{2} = 4$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -9$$
$$q = \frac{c}{a}$$
$$q = 20$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 9$$
$$x_{1} x_{2} = 20$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -9$$
$$q = \frac{c}{a}$$
$$q = 20$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 9$$
$$x_{1} x_{2} = 20$$
Sum and product of roots
[src]
sum
0 + 4 + 5
$$\left(0 + 4\right) + 5$$
=
9
$$9$$
product
1*4*5
$$1 \cdot 4 \cdot 5$$
=
20
$$20$$
20
The graph