Miraculous world of Numbers: June 2013

Thursday, June 20, 2013

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Some Important Problems related to Quadratic Equations:

a) If the sum of the root of the quadratic equation [1/(x + m)] + [1/(x + n)] = 1/p is 0, then show that the product of the roots is -[(m ² + n ²)/2]

Now by using the above method, we can easily solve the following examples.

A few more problems on Quadratic Equations related to factors will be discussed in the next Blog.

Some Important Problems related to Quadratic Equations:

a) If one root of the quadratic equation k x ² - 5 x + 2 = 0 is 4 times the other, then find " k "
Solution:

b) If the roots of the quadratic equation x ² + m x + n = 0 differ by 3, then prove that m ² = 4 n + 9
Solution:

c) If one root of the quadratic equation p x ² + x + p = 0 is the square of the other, then find prove that 1 + p q ( p + q - 3 ) = 0
Solution:

Hence Proved

A few more problems on Quadratic Equations related to factors will be discussed in the next Blog.