Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x^2-8=0
-
Equation 16*x^2/5-5=0
-
Equation x^2+14*x+40=0
-
Equation x^2-18=7x
- Express {x} in terms of y where:
- 12*x+2*y=-9
- 2*x+6*y=-2
- -19*x-16*y=3
- -18*x+10*y=12
-
Identical expressions
- x^ two +7x+ ten = zero
- x squared plus 7x plus 10 equally 0
- x to the power of two plus 7x plus ten equally zero
- x2+7x+10=0
- x²+7x+10=0
- x to the power of 2+7x+10=0
- x^2+7x+10=O
-
Similar expressions
- x^2+7x-10=0
- x^2-7x+10=0
x^2+7x+10=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
$$a = 1$$
$$b = 7$$
$$c = 10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2$$
$$x_{2} = -5$$
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
$$a = 1$$
$$b = 7$$
$$c = 10$$
, then
D = b^2 - 4 * a * c =
(7)^2 - 4 * (1) * (10) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2$$
$$x_{2} = -5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 7$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = 10$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 7$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = 10$$
Sum and product of roots
[src]
sum
-5 - 2
$$-5 - 2$$
=
-7
$$-7$$
product
-5*(-2)
$$- -10$$
=
10
$$10$$
10
The graph