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How to use it?
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Equation 17x+2x^2+21=0
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- 17x-2x^2+21=0
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17x+2x^2+21=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
$$a = 2$$
$$b = 17$$
$$c = 21$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{3}{2}$$
$$x_{2} = -7$$
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
$$a = 2$$
$$b = 17$$
$$c = 21$$
, then
D = b^2 - 4 * a * c =
(17)^2 - 4 * (2) * (21) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{3}{2}$$
$$x_{2} = -7$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} + 17 x\right) + 21 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{17 x}{2} + \frac{21}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{17}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{21}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{17}{2}$$
$$x_{1} x_{2} = \frac{21}{2}$$
$$\left(2 x^{2} + 17 x\right) + 21 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{17 x}{2} + \frac{21}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{17}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{21}{2}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{17}{2}$$
$$x_{1} x_{2} = \frac{21}{2}$$
Sum and product of roots
[src]
sum
-7 - 3/2
$$-7 - \frac{3}{2}$$
=
-17/2
$$- \frac{17}{2}$$
product
-7*(-3) ------- 2
$$- \frac{-21}{2}$$
=
21/2
$$\frac{21}{2}$$
21/2
The graph