Mister Exam
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36x^2-60x+25=0x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(36 x^{2} - 60 x\right) + 25 = 0 x$$
to
$$0 x + \left(\left(36 x^{2} - 60 x\right) + 25\right) = 0$$
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
$$a = 36$$
$$b = -60$$
$$c = 25$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = \frac{5}{6}$$
left part with negative sign.
The equation is transformed from
$$\left(36 x^{2} - 60 x\right) + 25 = 0 x$$
to
$$0 x + \left(\left(36 x^{2} - 60 x\right) + 25\right) = 0$$
This equation is of the form
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
$$a = 36$$
$$b = -60$$
$$c = 25$$
, then
D = b^2 - 4 * a * c =
(-60)^2 - 4 * (36) * (25) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --60/2/(36)
$$x_{1} = \frac{5}{6}$$
Vieta's Theorem
rewrite the equation
$$\left(36 x^{2} - 60 x\right) + 25 = 0 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{3} + \frac{25}{36} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{25}{36}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{3}$$
$$x_{1} x_{2} = \frac{25}{36}$$
$$\left(36 x^{2} - 60 x\right) + 25 = 0 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{5 x}{3} + \frac{25}{36} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{5}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{25}{36}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{5}{3}$$
$$x_{1} x_{2} = \frac{25}{36}$$
Sum and product of roots
[src]
sum
5/6
$$\frac{5}{6}$$
=
5/6
$$\frac{5}{6}$$
product
5/6
$$\frac{5}{6}$$
=
5/6
$$\frac{5}{6}$$
5/6