What is the discriminant of x^2 + 3x + 1 = 0 ?

√5

Step-by-step explanation:

x^2 + 3x + 1 = 0

Yo find discriminant

The discriminant helps us to determine the number of solutions to a quadratic equation

The general formula for solving quadratic equation is

x = -b+-(√b^2 -4ac)/2a

(√b^2 -4ac) gives the determinant

From the equation, a =1 (the coefficient of x^2

b = 3, the coefficient of x

c = 1, the constant

√b^2 -4ac =√3^2- 4×1×1

=√5

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

-2 is the right