Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x+19=12
-
Equation -x-7=x
-
Equation (x+2)/9=(x-3)/2
-
Equation 3(x+3)=2x+5
- Express {x} in terms of y where:
- -4*x+6*y=-7
- 10*x-18*y=-11
- -4*x-8*y=-20
- -9*x+11*y=9
-
Identical expressions
- 64x^ two - nine = zero
- 64x squared minus 9 equally 0
- 64x to the power of two minus nine equally zero
- 64x2-9=0
- 64x²-9=0
- 64x to the power of 2-9=0
- 64x^2-9=O
-
Similar expressions
- 64x^2+9=0
64x^2-9=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
$$a = 64$$
$$b = 0$$
$$c = -9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{3}{8}$$
$$x_{2} = - \frac{3}{8}$$
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
$$a = 64$$
$$b = 0$$
$$c = -9$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (64) * (-9) = 2304
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{3}{8}$$
$$x_{2} = - \frac{3}{8}$$
Vieta's Theorem
rewrite the equation
$$64 x^{2} - 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{9}{64} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{9}{64}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{9}{64}$$
$$64 x^{2} - 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{9}{64} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{9}{64}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{9}{64}$$
Sum and product of roots
[src]
sum
-3/8 + 3/8
$$- \frac{3}{8} + \frac{3}{8}$$
=
0
$$0$$
product
-3*3 ---- 8*8
$$- \frac{9}{64}$$
=
-9/64
$$- \frac{9}{64}$$
-9/64