Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 4(5x+2)=10(2x-3)+15
-
Equation x^2-4x=0
-
Equation x^2-7*x+12=0
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Equation x^2-5x-14=0
- Express {x} in terms of y where:
- 2*x+3*y=14
- -18*x+8*y=-2
- 6*x+17*y=-11
- -9*x+5*y=-2
-
Identical expressions
- t^ two +5t- fourteen = zero
- t squared plus 5t minus 14 equally 0
- t to the power of two plus 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
$$t_{1} = 2$$
$$t_{2} = -7$$
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
$$t_{1} = 2$$
$$t_{2} = -7$$
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
-7 + 2
$$-7 + 2$$
=
-5
$$-5$$
product
-7*2
$$- 14$$
=
-14
$$-14$$
-14