In September, the fourth digit of the code number is 2 more than the four digit of the code number based on prime factors of 225 the prime factors of what number were used for the code in September

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Ashu638

02.10.2022

Mathematics

${3x}^{2} - 5x = - 8 \\ {3x}^{2} - 5x + 8 = 0$

This equation has the next form:

${ax}^{2} + bx + c = 0$

To find if the equation has two complex solutions we have to check if the discriminant is negative, as follows:

${b}^{2} - 4ac \\ ( { - 5})^{2} - 4 \: . \: 3 \: . \: 8 = 25 - 96 = - 71 < 0$

Then, the first case has two complex solutions.

In the second case,

${2x}^{2} = 6x - 5 \\ {2x}^{2} - 6x + 5 = 0$

The discriminant in this case is:

$( { - 6})^{2} - 4 \: . \: 2 \: . \: 5 = 36 - 40 = - 4 < 0$

Then, the second case has two complex solutions.

In the third case,

$12x = {9x}^{2} + 4 \\ { - 9x}^{2} + 12x - 4 = 0$

The discriminant in this case is:

${12}^{2} - 4 \: . \: ( - 9) \: . \: ( - 4) = 144 - 144 = 0$

Then, the third case has two real solutions.

In the fourth case,

${ - x}^{2} - 10x = 34 \\ { - x}^{2} - 10x - 34 = 0$

The discriminant in this case is:

$( { - 10})^{2} - 4 \: . \: ( - 1) \: . \: ( - 34) = 100 - 136 = - 36 < 0$

Then, the fourth case has two complex solutions.

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