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- Equation:
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Equation 6*x^2+x-7=0
-
Equation (x^2-9)^2+(x^2+x-6)^2=0
-
Equation 15*x^2-4*x-3=0
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Equation (x-5)=(x+10)^2
- Express {x} in terms of y where:
- 2*x+20*y=16
- -15*x-12*y=17
- -20*x+5*y=-11
- 2*x+10*y=-5
- Graphing y =:
- 6*x^2+x-7
-
Identical expressions
- six *x^ two +x- seven = zero
- 6 multiply by x squared plus x minus 7 equally 0
- six multiply by x to the power of two plus x minus seven equally zero
- 6*x2+x-7=0
- 6*x²+x-7=0
- 6*x to the power of 2+x-7=0
- 6x^2+x-7=0
- 6x2+x-7=0
- 6*x^2+x-7=O
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Similar expressions
- 6*x^2+x+7=0
- 6*x^2-x-7=0
6*x^2+x-7=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
$$a = 6$$
$$b = 1$$
$$c = -7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = - \frac{7}{6}$$
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
$$a = 6$$
$$b = 1$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (6) * (-7) = 169
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = - \frac{7}{6}$$
Vieta's Theorem
rewrite the equation
$$\left(6 x^{2} + x\right) - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{6} - \frac{7}{6} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{6}$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{6}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{6}$$
$$x_{1} x_{2} = - \frac{7}{6}$$
$$\left(6 x^{2} + x\right) - 7 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{6} - \frac{7}{6} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{6}$$
$$q = \frac{c}{a}$$
$$q = - \frac{7}{6}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{6}$$
$$x_{1} x_{2} = - \frac{7}{6}$$
Sum and product of roots
[src]
sum
1 - 7/6
$$- \frac{7}{6} + 1$$
=
-1/6
$$- \frac{1}{6}$$
product
-7/6
$$- \frac{7}{6}$$
=
-7/6
$$- \frac{7}{6}$$
-7/6
The graph