Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2*(10x-9)^2-8*(10x-9)+8=0
- Equation 3(tg^2(x)-1)*sqrt(-5cosx)=0
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Equation sin(5x)=√2\2
- Equation t^2-5t-14=0
- Express {x} in terms of y where:
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- 9*x-18*y=6
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Identical expressions
- t^ two -5t- fourteen = zero
- t squared minus 5t minus 14 equally 0
- t to the power of two minus 5t minus fourteen equally zero
- t2-5t-14=0
- t²-5t-14=0
- t to the power of 2-5t-14=0
- t^2-5t-14=O
-
Similar expressions
- t^2-5t+14=0
- t^2+5t-14=0
t^2-5t-14=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:
$$t_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$t_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -5$$
$$c = -14$$
, then
Because D > 0, then the equation has two roots.
or
$$t_{1} = 7$$
$$t_{2} = -2$$
a*t^2 + b*t + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$t_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$t_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -5$$
$$c = -14$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (-14) = 81
Because D > 0, then the equation has two roots.
t1 = (-b + sqrt(D)) / (2*a)
t2 = (-b - sqrt(D)) / (2*a)
or
$$t_{1} = 7$$
$$t_{2} = -2$$
Vieta's Theorem
it is reduced quadratic equation
$$p t + q + t^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = -14$$
Vieta Formulas
$$t_{1} + t_{2} = - p$$
$$t_{1} t_{2} = q$$
$$t_{1} + t_{2} = 5$$
$$t_{1} t_{2} = -14$$
$$p t + q + t^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = -14$$
Vieta Formulas
$$t_{1} + t_{2} = - p$$
$$t_{1} t_{2} = q$$
$$t_{1} + t_{2} = 5$$
$$t_{1} t_{2} = -14$$
Sum and product of roots
[src]
sum
-2 + 7
$$-2 + 7$$
=
5
$$5$$
product
-2*7
$$- 14$$
=
-14
$$-14$$
-14