Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4*x=0
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Equation 7*x=0
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Equation 4x+3(x-7)=5
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Equation 3x-2=x+4
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Identical expressions
- five *x^ two - thirty-five = zero
- 5 multiply by x squared minus 35 equally 0
- five multiply by x to the power of two minus thirty minus five equally zero
- 5*x2-35=0
- 5*x²-35=0
- 5*x to the power of 2-35=0
- 5x^2-35=0
- 5x2-35=0
- 5*x^2-35=O
-
Similar expressions
- 5*x^2+35=0
5*x^2-35=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
$$a = 5$$
$$b = 0$$
$$c = -35$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{7}$$
$$x_{2} = - \sqrt{7}$$
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
$$a = 5$$
$$b = 0$$
$$c = -35$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (5) * (-35) = 700
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{7}$$
$$x_{2} = - \sqrt{7}$$
Vieta's Theorem
rewrite the equation
$$5 x^{2} - 35 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 7 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -7$$
$$5 x^{2} - 35 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 7 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -7$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -7$$
Sum and product of roots
[src]
sum
___ ___ - \/ 7 + \/ 7
$$- \sqrt{7} + \sqrt{7}$$
=
0
$$0$$
product
___ ___ -\/ 7 *\/ 7
$$- \sqrt{7} \sqrt{7}$$
=
-7
$$-7$$
-7
Rapid solution
[src]
___ x1 = -\/ 7
$$x_{1} = - \sqrt{7}$$
___ x2 = \/ 7
$$x_{2} = \sqrt{7}$$
x2 = sqrt(7)
The graph