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Similar expressions
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-5/2*x^2-13/2*x+3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
2 5*x 13*x - ---- - ---- + 3 = 0 2 2
$$\left(- \frac{5 x^{2}}{2} - \frac{13 x}{2}\right) + 3 = 0$$
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
$$a = - \frac{5}{2}$$
$$b = - \frac{13}{2}$$
$$c = 3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -3$$
$$x_{2} = \frac{2}{5}$$
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
$$a = - \frac{5}{2}$$
$$b = - \frac{13}{2}$$
$$c = 3$$
, then
D = b^2 - 4 * a * c =
(-13/2)^2 - 4 * (-5/2) * (3) = 289/4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -3$$
$$x_{2} = \frac{2}{5}$$
Vieta's Theorem
rewrite the equation
$$\left(- \frac{5 x^{2}}{2} - \frac{13 x}{2}\right) + 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{13 x}{5} - \frac{6}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{13}{5}$$
$$q = \frac{c}{a}$$
$$q = - \frac{6}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{13}{5}$$
$$x_{1} x_{2} = - \frac{6}{5}$$
$$\left(- \frac{5 x^{2}}{2} - \frac{13 x}{2}\right) + 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{13 x}{5} - \frac{6}{5} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{13}{5}$$
$$q = \frac{c}{a}$$
$$q = - \frac{6}{5}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{13}{5}$$
$$x_{1} x_{2} = - \frac{6}{5}$$
Sum and product of roots
[src]
sum
-3 + 2/5
$$-3 + \frac{2}{5}$$
=
-13/5
$$- \frac{13}{5}$$
product
-3*2 ---- 5
$$- \frac{6}{5}$$
=
-6/5
$$- \frac{6}{5}$$
-6/5