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Re: What is the value of x? [#permalink]
harish1986 wrote:
What is the value of x?

1) \(3x^2-8x-35=0\)
2) \(x^2 - 3x=7x-25\)


2) [m]x^2 - 3x=7x-25 => x = 5 => SUFFICIENT

OA: B
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What is the value of x? [#permalink]
harish1986 wrote:
What is the value of x?

1) \(3x^2-8x-35=0\)
2) \(x^2 - 3x=7x-25\)


A quadratic can have at most 2 real roots, 1 real root with multiplicity of 2, or 0 real roots. To check whether the quadratic has real roots, approximate the discriminant,\(\sqrt{b^2-4*a*c}\), to see if it is non-negative. The product of the real roots of a quadratic, \(a*x^2+b*x+c = 0\), is given by \(\frac{c}{a}.\) To establish sufficiency this quadratic should have one real root with multiplicity of 2. To check quickly whether the quadratic has 1 root, check first to see if b is an integer and then check to see if \(\sqrt{\frac{c}{a}}\) is rational. If it is easy to calculate the discriminant and it is zero, then it will have one root and checking whether \(\sqrt{\frac{c}{a}}\) is rational is unnecessary.

(Statement 1): In this statement c=-35 and a=3 --> \(\sqrt{\frac{-35}{3}}\) = non-rational number. This statement is insufficient

(Statement 2): \(x^2 - 3x=7x-25\) --> \(x^2-10*x+25=0.\) In this statement c=25 and a=1 --> \(\sqrt{\frac{25}{1}}\) = rational number. This statement is sufficient. Also since the discriminant is zero, this statement is sufficient. Correct answer choice is B.

Originally posted by bhaskar438 on 17 Oct 2015, 22:37.
Last edited by bhaskar438 on 19 Oct 2015, 09:54, edited 1 time in total.
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Re: What is the value of x? [#permalink]
Please change the answer from Choice C to Choice B.
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Re: What is the value of x? [#permalink]
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bhaskar438 wrote:
Please change the answer from Choice C to Choice B.

_______________
Edited. Thank you.
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Re: What is the value of x? [#permalink]
Easy one! answer is B

You don't need to find the values of the solutions.
By just knowing that (b^2 - 4*a*c) equal zero tells you that answer statement (2) has a unique solution.
statement (1) deos not.
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Re: What is the value of x? [#permalink]
harish1986 wrote:
What is the value of x?

1) \(3x^2-8x-35=0\)
2) \(x^2 - 3x=7x-25\)


Discriminant (sqrt(b2-4ac)

D=0; one root,
D<0; no solutions
D=0; 1 solution
D>1; 2 solutions
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Re: What is the value of x? [#permalink]
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