Solve The Following Equation

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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.

Byjus IAS


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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