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- Equation:
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Equation 25+10x-8x^2=0
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Equation x+76=978+359
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Identical expressions
- twenty-five +1 zero x-8x^ two =0
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Similar expressions
- 25+10x+8x^2=0
- 25-10x-8x^2=0
25+10x-8x^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
$$a = -8$$
$$b = 10$$
$$c = 25$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{5}{4}$$
$$x_{2} = \frac{5}{2}$$
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
$$a = -8$$
$$b = 10$$
$$c = 25$$
, then
D = b^2 - 4 * a * c =
(10)^2 - 4 * (-8) * (25) = 900
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{5}{4}$$
$$x_{2} = \frac{5}{2}$$
Vieta's Theorem
rewrite the equation
$$- 8 x^{2} + \left(10 x + 25\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{4} - \frac{25}{8} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{4}$$
$$q = \frac{c}{a}$$
$$q = - \frac{25}{8}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{4}$$
$$x_{1} x_{2} = - \frac{25}{8}$$
$$- 8 x^{2} + \left(10 x + 25\right) = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{4} - \frac{25}{8} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{4}$$
$$q = \frac{c}{a}$$
$$q = - \frac{25}{8}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{4}$$
$$x_{1} x_{2} = - \frac{25}{8}$$
Sum and product of roots
[src]
sum
-5/4 + 5/2
$$- \frac{5}{4} + \frac{5}{2}$$
=
5/4
$$\frac{5}{4}$$
product
-5*5 ---- 4*2
$$- \frac{25}{8}$$
=
-25/8
$$- \frac{25}{8}$$
-25/8
The graph