MATHEMATICS HIGH SCHOOL

If one of the zeros of 3x^2+5x+γ=0 is 4 times the other, then find the zero and value of k

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Let α be one of the zeros of the polynomial.

Other = 4α

α + 4α = - Coefficient of x / Coefficient of x² = -5/3

5α = -5/3

α = -5/3*5

α = -1/3

α * 4α = Constant term/Coefficient of x²

4α² = k / 3

$4*((-1)/(3))^(2)=(k)/(3)\n\n4*(1)/(9)=(k)/(3)\n\n4*(1)/(9)*3=k\n\n4*(1)/(3)=k\n\nk=(4)/(3)$

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Solve this system of equations by using an algebraic method.Equation:
y = 3x + 5
3x - y = 5

Answers

Answer:

Step-by-step explanation:

Substitute our first equation into the second equation. We are given y, so this is ideal of substitution method.

y = 3x + 5
3x - y = 5

3x - (3x + 5) = 5
3x - 3x - 5 = 5
-5 = 5

There is no solution for the system because after solving, the sides of the equation are not equal. We can further check this by writing the second equation in a "y = mx + b form, or slope-intercept form. This well tell use about the graphs of the equations.

3x - y = 5
-y = -3x + 5

y = 3x -5

When comparing with the first equation, we can see that the slope is 3 for both lines, but the y-intercept is different. This means we have two parallel lines that cross the y-axis at (0, 5) and (0, -5). From this, one can conclude there is no solution because parallel lines with different y-intercepts will never cross.

What is the domain of f(x)?What is the range of f(x)?
How is the domain and range of this function different from the other functions you have seen in this topic?