Mister Exam
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Identical expressions
- (-4x+ seven)(-x+ five)
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Similar expressions
- (-4x+7)(x+5)
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(-4x+7)(-x+5) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(5 - x\right) \left(7 - 4 x\right) = 0$$
We get the quadratic equation
$$4 x^{2} - 27 x + 35 = 0$$
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
$$a = 4$$
$$b = -27$$
$$c = 35$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = \frac{7}{4}$$
$$\left(5 - x\right) \left(7 - 4 x\right) = 0$$
We get the quadratic equation
$$4 x^{2} - 27 x + 35 = 0$$
This equation is of the form
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
$$a = 4$$
$$b = -27$$
$$c = 35$$
, then
D = b^2 - 4 * a * c =
(-27)^2 - 4 * (4) * (35) = 169
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = \frac{7}{4}$$
Sum and product of roots
[src]
sum
5 + 7/4
$$\frac{7}{4} + 5$$
=
27/4
$$\frac{27}{4}$$
product
5*7 --- 4
$$\frac{5 \cdot 7}{4}$$
=
35/4
$$\frac{35}{4}$$
35/4