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Similar expressions
- 3x^2+17x+10=0
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3x^2-17x+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
$$a = 3$$
$$b = -17$$
$$c = 10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
Simplify
$$x_{2} = \frac{2}{3}$$
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
$$a = 3$$
$$b = -17$$
$$c = 10$$
, then
D = b^2 - 4 * a * c =
(-17)^2 - 4 * (3) * (10) = 169
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
$$x_{2} = \frac{2}{3}$$
Simplify
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 17 x + 10 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{17 x}{3} + \frac{10}{3} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{17}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{10}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{17}{3}$$
$$x_{1} x_{2} = \frac{10}{3}$$
$$3 x^{2} - 17 x + 10 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{17 x}{3} + \frac{10}{3} = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{17}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{10}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{17}{3}$$
$$x_{1} x_{2} = \frac{10}{3}$$
Sum and product of roots
[src]
sum
0 + 2/3 + 5
$$\left(0 + \frac{2}{3}\right) + 5$$
=
17/3
$$\frac{17}{3}$$
product
1*2/3*5
$$1 \cdot \frac{2}{3} \cdot 5$$
=
10/3
$$\frac{10}{3}$$
10/3
The graph