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How to use it?
- Equation:
- Equation xy
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Equation x^2+x-20=0
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Equation 5x^2=-80+40x
- Equation 16k^2+9-24k=0
- Express {x} in terms of y where:
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Identical expressions
- 16k^ two + nine -24k= zero
- 16k squared plus 9 minus 24k equally 0
- 16k to the power of two plus nine minus 24k equally zero
- 16k2+9-24k=0
- 16k²+9-24k=0
- 16k to the power of 2+9-24k=0
- 16k^2+9-24k=O
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Similar expressions
- 16k^2+9+24k=0
- 16k^2-9-24k=0
16k^2+9-24k=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:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 16$$
$$b = -24$$
$$c = 9$$
, then
Because D = 0, then the equation has one root.
$$k_{1} = \frac{3}{4}$$
a*k^2 + b*k + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 16$$
$$b = -24$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(-24)^2 - 4 * (16) * (9) = 0
Because D = 0, then the equation has one root.
k = -b/2a = --24/2/(16)
$$k_{1} = \frac{3}{4}$$
Vieta's Theorem
rewrite the equation
$$- 24 k + \left(16 k^{2} + 9\right) = 0$$
of
$$a k^{2} + b k + c = 0$$
as reduced quadratic equation
$$k^{2} + \frac{b k}{a} + \frac{c}{a} = 0$$
$$k^{2} - \frac{3 k}{2} + \frac{9}{16} = 0$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{3}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{16}$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = \frac{3}{2}$$
$$k_{1} k_{2} = \frac{9}{16}$$
$$- 24 k + \left(16 k^{2} + 9\right) = 0$$
of
$$a k^{2} + b k + c = 0$$
as reduced quadratic equation
$$k^{2} + \frac{b k}{a} + \frac{c}{a} = 0$$
$$k^{2} - \frac{3 k}{2} + \frac{9}{16} = 0$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{3}{2}$$
$$q = \frac{c}{a}$$
$$q = \frac{9}{16}$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = \frac{3}{2}$$
$$k_{1} k_{2} = \frac{9}{16}$$
Sum and product of roots
[src]
sum
3/4
$$\frac{3}{4}$$
=
3/4
$$\frac{3}{4}$$
product
3/4
$$\frac{3}{4}$$
=
3/4
$$\frac{3}{4}$$
3/4