Solve The Following Equation. The largest power of the variable in a quadratic equation, which is a polynomial equation of the second degree, is two. Ax2 + bx + c = 0, where a, b, and c are coefficients and x is variable, is how quadratic equations are expressed.

## Find the Roots Solve: **4x ^ 2 – 5x – 12 =** 0

To find the roots of the equation, we use the quadratic formula: x = (-b ± √(b^2 – 4ac)) / 2a.

This is the example, of the question – a = 4, b = -5, and c = -12. Plugging these values into the formula, we get:

x = (-(-5) ± √((-5)^2 – 4(4)(-12))) / 2(4)

x = (5 ± √169) / 8

Below are the very Simplifying this expression so you can understand, what we get:

x = (5 + 13) / 8 or x = (5 – 13) / 8

This is the roots of the equation are x = 3/2 and x = -1.

## Find The Remainder When x3+3×2+3x+1 is Divided By x+1

To find the remainder when x³ + 3x² + 3x + 1 is divided by x + 1, we can use polynomial long division.

The first step is to set up the division, with x + 1 as the divisor and x³ + 3x² + 3x + 1 as the dividend:

x² + 2x + 1

x + 1 | x³ + 3x² + 3x + 1

-x³ – x²

———–

2x² + 3x + 1

2x² + 2x

———

x + 1

The result of the division is x² + 2x + 1 with a remainder of x + 1. Therefore, the remainder when x³ + 3x² + 3x + 1 is divided by x + 1 is x + 1.

## If 3x+5y=9 and 5x+3y=7 What is The Value of x+y

**To find the value of x + y, we need to solve the system of equations:**

3x + 5y = 9 …(1)

5x + 3y = 7 …(2)

We can solve this system by using the elimination method. To do so, we can multiply equation (1) by 3 and equation (2) by 5, so that the coefficients of x in each equation will be equal and opposite:

9x + 15y = 27 …(3) (multiplying equation (1) by 3)

25x + 15y = 35 …(4) (multiplying equation (2) by 5)

**Now we can subtract equation (3) from equation (4) to eliminate y:**

25x + 15y – (9x + 15y) = 35 – 27

16x = 8

x = 1/2

**Substituting x = 1/2 into equation (1) or (2), we can find y:**

3(1/2) + 5y = 9

5y = 8.5

y = 1.7

Therefore, x + y = 1/2 + 1.7 = 2.2.

## 58. 2x ^ 2 – 9x ^ 2; 5 – 3x + y + 6

**It looks like you have provided two separate expressions:**

2x^2 – 9x^2

5 – 3x + y + 6

**To Solve the question, we can combine the like terms 2x^2 and -9x^2 by subtracting them:**

2x^2 – 9x^2 = -7x^2

**Therefore, the simplified form of the first expression is -7x^2.**

For the second expression, 5 – 3x + y + 6, we can combine the constant terms 5 and 6 to get 11:

5 – 3x + y + 6 = 11 – 3x + y

**Therefore, the simplified form of the second expression is 11 – 3x + y.**

## What is The Equation of X-Axis

The equation of the x-axis is y = 0. This is because the x-axis is the horizontal line that cut the y-axis at the point (0,0), and all points on the x-axis have a y-coordinate of 0. So the equation y = 0 represents the set of all points that lie on the x-axis.

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