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A B C of Solving Quadratic Equation
An expression of the type ax² + bx + c = 0, (a ≠ 0) is called a quadratic equation in the variable x.
The equation ax² + bx + c = 0 is called the general form (or, standard form)
We can solve a quadratic equation by (1) factoring or by (2) applying the formula.
The formula for finding the roots of the quadratic equation is as follows
x = (- b ± √ (b² – 4 ac)) / 2 a
Now we will discuss how to fix the applied issues. Due to the wide variety of problems applied, there is no single resolution technique that works in all cases. However, the following suggestion has proven useful.
Step: 1 Read the problem carefully and determine what quantity(s) should be found.
Step: 2 Assign a variable name to the quantity.
Step: 3 Try to express the problem algebraically, determine which expressions are equal and write the necessary equation(s).
Step: 3 solve the resulting equation(s)
Now move on to a simple problem based on forming a quadratic equation and solving
Problem: The denominator of a fraction is more than twice the numerator. If the sum of the fraction and its inverse is 58/21. Find the fraction.
Let the numerator of the fraction x (x be an element of I )
So its denominator is (2x + 1).
So the fraction is x / (2x + 1))
And the inverse would be (2 x + 1) / x
According to the problem:
(X / (2x + 1)) + ((2x + 1) / x) = ( 58 / 21 )
(X² + (2x + 1)²) / (x + (2x + 1)) = ( 58 / 21)
[L. C. D is = ( x + ( 2x + 1 ) ]
21 ( x² + 4 x² + 4x + 1 ) = 58 x ( 2x + 1 )
105x² + 84x + 21 = 116x² + 58x
11x² – 26x – 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) (11x + 7) = 0
Either ( x – 3 ) = 0 , or ( 11x + 7 ) = 0 [ using zero factor theorem ]
x = 3,
Of, (11x + 7) = 0
We get, x = – (7/11)
But x is an integer, neglect 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 the square of his son’s age. Eight years therefore the age of the man will be 4 years older than three times the age of his son. Find their 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 time. Any reasonably good math teacher should do.
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