Mister Exam
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- 25*x^2+30*x+9=0
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25*x^2-30*x+9=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
$$a = 25$$
$$b = -30$$
$$c = 9$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = \frac{3}{5}$$
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
$$a = 25$$
$$b = -30$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(-30)^2 - 4 * (25) * (9) = 0
Because D = 0, then the equation has one root.
x = -b/2a = --30/2/(25)
$$x_{1} = \frac{3}{5}$$
Vieta's Theorem
rewrite the equation
$$\left(25 x^{2} - 30 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{6 x}{5} + \frac{9}{25} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{6}{5}$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{25}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{6}{5}$$
$$x_{1} x_{2} = \frac{9}{25}$$
$$\left(25 x^{2} - 30 x\right) + 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{6 x}{5} + \frac{9}{25} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{6}{5}$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{25}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{6}{5}$$
$$x_{1} x_{2} = \frac{9}{25}$$
Sum and product of roots
[src]
sum
3/5
$$\frac{3}{5}$$
=
3/5
$$\frac{3}{5}$$
product
3/5
$$\frac{3}{5}$$
=
3/5
$$\frac{3}{5}$$
3/5
The graph