Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -5x=30
-
Equation 3*x^2=18*x
-
Equation 16*x^2-9=0
-
Equation 0*x=5
- Express {x} in terms of y where:
- 10*x-18*y=-6
- 3*x-12*y=-14
- 16*x+11*y=-14
- -4*x+20*y=-14
- Factor polynomial:
- 16*x^2-9
-
Identical expressions
- sixteen *x^ two - nine = zero
- 16 multiply by x squared minus 9 equally 0
- sixteen multiply by x to the power of two minus nine equally zero
- 16*x2-9=0
- 16*x²-9=0
- 16*x to the power of 2-9=0
- 16x^2-9=0
- 16x2-9=0
- 16*x^2-9=O
-
Similar expressions
- 16*x^2+9=0
16*x^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
$$a = 16$$
$$b = 0$$
$$c = -9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{3}{4}$$
$$x_{2} = - \frac{3}{4}$$
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
$$a = 16$$
$$b = 0$$
$$c = -9$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (16) * (-9) = 576
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{3}{4}$$
$$x_{2} = - \frac{3}{4}$$
Vieta's Theorem
rewrite the equation
$$16 x^{2} - 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{9}{16} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{9}{16}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{9}{16}$$
$$16 x^{2} - 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{9}{16} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{9}{16}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = - \frac{9}{16}$$
Sum and product of roots
[src]
sum
-3/4 + 3/4
$$- \frac{3}{4} + \frac{3}{4}$$
=
0
$$0$$
product
-3*3 ---- 4*4
$$- \frac{9}{16}$$
=
-9/16
$$- \frac{9}{16}$$
-9/16
The graph