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Re: Inequalities, how to crack solve this [#permalink]
23 Aug 2011, 22:48

Expert's post

i guess the source is manhattan...anywayz i got struck with a simple technique...picking up numbers.. consider (x+1)^2=x^2+2x+1 (x+2)^2=x^2+4x+4 ....similarly u can go for other numbers as well..then analyse the values of a and b by considering the given options.. ans e _________________

Re: Inequalities, how to crack solve this [#permalink]
23 Aug 2011, 23:06

x^2+ax+b => has only 1 solution So the equation should be of the form x^2 + 2Bx + B^2=0 (i.e) (x+B)^2=0ORx^2 - 2Bx + B^2=0 (i.e) (x-B)^2=0 Hence substitute in place of B^2 = b and in place of 2B = a we get a=2\sqrt{b} => a^2=4b [Squaring on both sides] => b=a^2/4 (E)

Re: Inequalities, how to crack solve this [#permalink]
24 Aug 2011, 00:47

naaga wrote:

how did you take a=2sqrtb, from the above equation ?

Since the given equation is a quadratic equation, there would always be 2 roots (solution) for it. eg: (x+p)(x+q) But the question says the equation has only 1 solution. This could be possible only when both the roots are same. i.e (x+p)(x+p). This can be written as (x+p)^2 We know the formula for this i.e (x+p)^2 = x^2+2px+p^2 Now visualize the given equation (x^2+ax+b) with the above formula: Coefficient of x^2 = 1 Coefficient of x = a (which is nothing but 2p) Constant term (i.e the p^2) = b Hence we can write: p^2=b => p=\sqrt{b} => a=2p = 2\sqrt{b}

Re: Inequalities, how to crack solve this [#permalink]
24 Aug 2011, 11:31

the root must be -a/2. (Quadratic equation with only one root) Substituting the -a/2 in the equation & equating it to 0. You will get b= a^2 / 4 Hence, E is the answer. _________________

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