Mister Exam
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Identical expressions
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Similar expressions
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4.9x^2+4.2x+0.9=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 49*x 21*x 9 ----- + ---- + -- = 0 10 5 10
$$\left(\frac{49 x^{2}}{10} + \frac{21 x}{5}\right) + \frac{9}{10} = 0$$
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
$$a = \frac{49}{10}$$
$$b = \frac{21}{5}$$
$$c = \frac{9}{10}$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = - \frac{3}{7}$$
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
$$a = \frac{49}{10}$$
$$b = \frac{21}{5}$$
$$c = \frac{9}{10}$$
, then
D = b^2 - 4 * a * c =
(21/5)^2 - 4 * (49/10) * (9/10) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -21/5/2/(49/10)
$$x_{1} = - \frac{3}{7}$$
Vieta's Theorem
rewrite the equation
$$\left(\frac{49 x^{2}}{10} + \frac{21 x}{5}\right) + \frac{9}{10} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{6 x}{7} + \frac{9}{49} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{6}{7}$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{49}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{6}{7}$$
$$x_{1} x_{2} = \frac{9}{49}$$
$$\left(\frac{49 x^{2}}{10} + \frac{21 x}{5}\right) + \frac{9}{10} = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{6 x}{7} + \frac{9}{49} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{6}{7}$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{49}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{6}{7}$$
$$x_{1} x_{2} = \frac{9}{49}$$
Sum and product of roots
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sum
-3/7
$$- \frac{3}{7}$$
=
-3/7
$$- \frac{3}{7}$$
product
-3/7
$$- \frac{3}{7}$$
=
-3/7
$$- \frac{3}{7}$$
-3/7