Mister Exam
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Identical expressions
- -x^ two -7x+ ten = zero
- minus x squared minus 7x plus 10 equally 0
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- -x²-7x+10=0
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- -x^2-7x+10=O
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Similar expressions
- -x^2-7x-10=0
- x^2-7x+10=0
- -x^2+7x+10=0
-x^2-7x+10=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
$$a = -1$$
$$b = -7$$
$$c = 10$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{\sqrt{89}}{2} - \frac{7}{2}$$
$$x_{2} = - \frac{7}{2} + \frac{\sqrt{89}}{2}$$
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
$$a = -1$$
$$b = -7$$
$$c = 10$$
, then
D = b^2 - 4 * a * c =
(-7)^2 - 4 * (-1) * (10) = 89
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{\sqrt{89}}{2} - \frac{7}{2}$$
$$x_{2} = - \frac{7}{2} + \frac{\sqrt{89}}{2}$$
Vieta's Theorem
rewrite the equation
$$\left(- x^{2} - 7 x\right) + 10 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 7 x - 10 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 7$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = -10$$
$$\left(- x^{2} - 7 x\right) + 10 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 7 x - 10 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 7$$
$$q = \frac{c}{a}$$
$$q = -10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -7$$
$$x_{1} x_{2} = -10$$
Sum and product of roots
[src]
sum
____ ____ 7 \/ 89 7 \/ 89 - - + ------ + - - - ------ 2 2 2 2
$$\left(- \frac{\sqrt{89}}{2} - \frac{7}{2}\right) + \left(- \frac{7}{2} + \frac{\sqrt{89}}{2}\right)$$
=
-7
$$-7$$
product
/ ____\ / ____\ | 7 \/ 89 | | 7 \/ 89 | |- - + ------|*|- - - ------| \ 2 2 / \ 2 2 /
$$\left(- \frac{7}{2} + \frac{\sqrt{89}}{2}\right) \left(- \frac{\sqrt{89}}{2} - \frac{7}{2}\right)$$
=
-10
$$-10$$
-10
Rapid solution
[src]
____
7 \/ 89
x1 = - - + ------
2 2
$$x_{1} = - \frac{7}{2} + \frac{\sqrt{89}}{2}$$
____
7 \/ 89
x2 = - - - ------
2 2
$$x_{2} = - \frac{\sqrt{89}}{2} - \frac{7}{2}$$
x2 = -sqrt(89)/2 - 7/2