Quadratic querie

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Thu Oct 29, 2009 1:36 am

If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all values for k such that f (k+2)=g(2k) ?

Looks pretty simple..however I got stuck mid-way.
Got till K^2-4K-65=0
Does anyone know how to proceed further??

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Source: Beat The GMAT — Problem Solving | Thu Oct 29, 2009 1:36 am

NikolayZ: Master | Next Rank: 500 Posts; Posts: 124; Joined: Thu Jun 18, 2009 5:33 am; Thanked: 35 times

by NikolayZ » Thu Oct 29, 2009 1:47 am

Hey again !
You need to use quadratic formula for discriminant, to solve the quadratic equation without factoring.

D=b^2-4ac,
And roots of the equation will be
x12=(-bÂ±sqrt(b^2-4ac))/2a.
D=4+4*65=264
x1=(4+sqrt(264))/2, x2=(4-sqrt(264))/2.
You need to find the sum of the roots, so

x1+x2= (4+sqrt(264)+4-sqrt(264))/2 ==> (4+4)/2=4

Hope this helps.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: Quadratic querie

by Brent@GMATPrepNow » Sun Nov 01, 2009 2:32 pm

uptowngirl92 wrote:If f(x)=5x^2 and g(x)=x^2 + 12x + 85, what is the sum of all values for k such that f (k+2)=g(2k) ?

Looks pretty simple..however I got stuck mid-way.
Got till K^2-4K-65=0
Does anyone know how to proceed further??

You're almost there.
There's a nice rule that says, "If m and n are solutions to the equation x^2 + bx + c = 0, then m+n = -b

In the example k^2-4k-65=0, b=-4
So, m+n = -(-4) = 4

Brent Hanneson - Creator of GMATPrepNow.com

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NikolayZ: Master | Next Rank: 500 Posts; Posts: 124; Joined: Thu Jun 18, 2009 5:33 am; Thanked: 35 times

by NikolayZ » Sun Nov 01, 2009 11:55 pm

Brent ! great one. It is really discriminant terminating thing

But we have to be aware of the form of qudratic equation.
Equation must not have an "a" coefficient (a*x^2+bx+c) for this rule to work. I suppose.

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