Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation a*x=b
-
Equation 2-3(2+3x)=14
-
Equation x^2-x+8=0
-
Equation 2^x=7
- Express {x} in terms of y where:
- 8*x-4*y=10
- -17*x-5*y=-20
- 2*x+19*y=-7
- -4*x+7*y=-16
- Factor polynomial:
- x^2-3*x-10
- Factor squared:
- x^2-3*x-10
-
Identical expressions
- x^ two - three *x- ten = zero
- x squared minus 3 multiply by x minus 10 equally 0
- x to the power of two minus three multiply by x minus ten equally zero
- x2-3*x-10=0
- x²-3*x-10=0
- x to the power of 2-3*x-10=0
- x^2-3x-10=0
- x2-3x-10=0
- x^2-3*x-10=O
-
Similar expressions
- x^2-3*x+10=0
- x^2+3*x-10=0
x^2-3*x-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
$$a = 1$$
$$b = -3$$
$$c = -10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = -2$$
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
$$a = 1$$
$$b = -3$$
$$c = -10$$
, then
D = b^2 - 4 * a * c =
(-3)^2 - 4 * (1) * (-10) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = -2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = -10$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = -10$$
Sum and product of roots
[src]
sum
-2 + 5
$$-2 + 5$$
=
3
$$3$$
product
-2*5
$$- 10$$
=
-10
$$-10$$
-10
The graph