Quadratic Formula And the Section Formula

Quadratic Formula And the Section Formula

Education

Section Formula is an important formula in mathematics. Do you have any idea where we can use this formula in our life? Let’s learn about it. The section formula has application in simple machines like scissors that has a fixed point around which you move the scissor to cut any paper. So, this point is the section, for which you can use the section formula. Now, let us go through an example of this concept. You can learn more about it on cuemath.com

Let us say that XY is a line segment and P is the pivot that divides this segment into two sections of the ratio of m: n. Now, to express this statement in a mathematical term,  we have a formula called the section formula, which is:                    

  • (up2 + vp1)/(u + v)
  • (uq2 + vq1)/(u + v)

Therefore, coordinates of P {(up2 + vp1)/(u + v), (uq2 + vq1)/(u + v)}.

Example of the Section Formula

Assume that a marathon race is going to take place in Rajiv Garden, Delhi. The marked points are in the following way:

  • The first round of the race completes in ⅓rd part of the ground.
  • The second round of the race completes in 1/4th part of the ground.
  • The third part gets competed at 1/5th part of the ground.
  • Finally, the last part gets completed at the remaining part of the ground.

This is how sections are prepared for each round. Now, if we take the first round, then we can use the above formula in the ratio of 1: 3. Similarly, we can do for the remaining parts and get our desired answer by using the section formula.

Similarly, the Quadratic formula plays a crucial topic in Maths. It consists of coefficients and variables. Do you know what is the quadratic formula? Well, an equation that you can see below is a quadratic equation:

px2 + qx + r = 0

What are p, q, and r here? Well, these terms are called coefficients and ‘x’ is a variable. Here, coefficients are something that is a constant or an unchangeable value and ‘x’ can vary any number of times we wish to. Isn’t it so simple? So, now let us understand the concept of quadratic equations with the help of an example.

Example on the Quadratic Equations

The quadratic equation that we have mentioned above is a combination of coefficients, variables, and operators, like here we can an addition operator. Also, it happens that when this combination comes, we call it the mathematical expression or the arithmetic expression too.

Here, for example, a person walks 16 km on the first day, 4 km on the second day, 9 km on the third day, 3 km again on the fourth day, and so on. This pattern goes on alternatively, which shows that the person has variable walking distance in two consecutive days, which we call the variable ‘x’. The first day is x-sqaure and the second day is variable ‘x’.

Now, if we write the coefficients p, q, and r as 4, 5, and 6, respectively, they remain unchanged because they are constants. However, we can put any number of values of “x” because it is an unknown value and may/may not change.

So, this was about our arithmetic part, now, let us gain an insight into geometry. So, what so special do you find in geometry?

Well, geometry is something that helps you increase your visual power, i.e., imagination. Suppose there are two girls playing a see-saw game. You might have seen in a see-saw, there is a point in the mid of the line that balances the weight on either side of this segment. This pivot is the mid-section of the see-saw.

A very interesting geometry can be seen in this swing. However, if you wish to explain such a thing in mathematical terms, we have a formula called the section formula, which is explained above. 

Uneeb Khan

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