Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation (a-2)(b+5)=(a-2)b+(a-2)5
-
Equation x+5=0
-
Equation 4*x^2-25=0
-
Equation 8x-15=-12+5x
- Express {x} in terms of y where:
- -14*x+16*y=6
- -4*x-15*y=6
- 8*x-6*y=-18
- -5*x-14*y=18
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Identical expressions
- four *x^ two - twenty-five = zero
- 4 multiply by x squared minus 25 equally 0
- four multiply by x to the power of two minus twenty minus five equally zero
- 4*x2-25=0
- 4*x²-25=0
- 4*x to the power of 2-25=0
- 4x^2-25=0
- 4x2-25=0
- 4*x^2-25=O
-
Similar expressions
- 4*x^2+25=0
4*x^2-25=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
$$a = 4$$
$$b = 0$$
$$c = -25$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{5}{2}$$
$$x_{2} = - \frac{5}{2}$$
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
$$a = 4$$
$$b = 0$$
$$c = -25$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (4) * (-25) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5}{2}$$
$$x_{2} = - \frac{5}{2}$$
Vieta's Theorem
rewrite the equation
$$4 x^{2} - 25 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{25}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{25}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{25}{4}$$
$$4 x^{2} - 25 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{25}{4} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{25}{4}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{25}{4}$$
Sum and product of roots
[src]
sum
-5/2 + 5/2
$$- \frac{5}{2} + \frac{5}{2}$$
=
0
$$0$$
product
-5*5 ---- 2*2
$$- \frac{25}{4}$$
=
-25/4
$$- \frac{25}{4}$$
-25/4
The graph