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## A B C of Solving Quadratic Equation

An expression of the type ax ² + bx + c = 0, (a ≠ 0) is called a quadratic equation in the variable x.

The equation ax² + bx + c = 0 is called the general (or standard) form

We can solve a quadratic equation by (1) factoring or (2) applying the formula.

The formula for finding the roots of the quadratic equation is as follows

x = (- b ± √ (b ² – 4 ac) ) / 2 a

Now we will talk about how to solve applied problems. Due to the wide variety of applied problems, there is no single solution technique that works in all cases. However, the following suggestion proved helpful.

Step: 1 Read the problem carefully and determine which quantity(s) you need to find.

Step: 2 Assign a variable name to the amount.

Step: 3 try to express the problem algebraically, and also determine which expressions are equal and write the necessary equation(s).

Step: 3 solve the resulting equation(s).

Now go through a simple problem based on forming quadratic equations and solving

Problem: The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 58 / 21. Find the fraction.

Solution:

Let x be the numerator of the fraction (x be an element of I )

Then its denominator is (2x + 1).

So the fraction is x / (2x + 1))

And the reciprocal would be (2 x + 1) / x

Depending on the problem:

(X / (2 xs + 1)) + ((2 x + 1) / x) = ( 58 / 21 )

(X ² + (2 x + 1) ²) / (x + (2x + 1)) = ( 58 / 21)

[L. C. D is = ( x + ( 2x + 1 ) ]

21 ( x ² + 4 x ² + 4 x + 1 ) = 58 x ( 2x + 1 )

105 x² + 84 x + 21 = 116 x² + 58 x

11 x ² – 26 x – 21 = 0

11 x ² – (33 – 7) x – 21 = 0 [using middle term factorization]

11 x ²- 33 x + 7 x – 21 = 0

11 x ( x – 3 ) + 7 ( x – 3 ) = 0

(x – 3) (11 x + 7) = 0

Or ( x – 3 ) = 0 or ( 11x + 7 ) = 0 [ using zero factor theorem ]

x = 3,

From, (11x + 7) = 0

We get, x = – (7/11)

But x is an integer, neglect x = – (7 / 11)

Take x = 3

Therefore, the required fraction, (x / (2x + 1)) = (3 / (2 * 3 + 1))

= (3/7)

Now try the following:

A man’s age is twice the square of his child’s age. Eight years, therefore, the man’s age will be 4 years more than three times the age of his son. Find your current age?

If you can’t solve this problem, you probably need more practice. A good online tutor would be helpful if you plan to master this subject in a short period of time. Any reasonably good math tutor should do this.

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