How To Solve A Quadratic Equation By Quadratic Formula A B C of Solving Quadratic Equation

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A B C of Solving Quadratic Equation

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

The equation ax ² + bx + c = 0 is called general (or, general form)

We can solve the quadratic equation (1) by factorization or (2) by using the formula.

The method for finding the roots of a quadratic equation is as follows

x = (- b ± √ (b ² – 4 ac) ) / 2 a

Now we will discuss how to solve the problems used. Due to the wide range of problems used, there is no single solution that works in all cases. However, the following advice has proven helpful.

Step: 1 Read the problem carefully and see what quantity(s) need to be found.

Step: 2 assign a variable name to the size.

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

Step: 3 solve the resulting equation(s)

Now move on to a simple problem based on forming a quadratic equation and solving it

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

Solution:

Let the number of the fraction be x (x is an element of I )

Then its denominator is (2x + 1).

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

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

Problem wise:

(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 x ² + 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 a whole number, ignoring x = – (7 / 11)

Take x = 3

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

= (3 / 7)

Now try the following:

A man’s age is twice that of his son. Eight years old then the man’s age will be 4 years more than his son’s third. Find out their current age?

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

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