Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
Let f(x)=x2+bx+c,where b,c belong to R.If f(x) is a factor of both x4+6x2+25 and 3x4+4x2+28x+5,then the least value of f(x) is
a.2
b.3
c.5/2
d.4
Hi Menka,
Concept:
Herer the idea is to get a Quadratic Equation (so that you can find its minimum)
Now if f(x) is a factor of P(x) and Q(x), then f(x) should be a factor of any linear combination of P(x) and Q(x)-------- {this is obvious because, f(x) is indivdually a factor for both the functions}
Hence f(x) is factor of 3P(x) - Q(x) = 14x^2 - 28x + 70 = 14{x^2 - 2x + 5}
Now as f(x) is Quad, with co-eff od x^2 as 1, f(x) must be x^2 - 2x + 5.
ie f(x) = (x-1)^2 + 4.
So minimum value is 4.
Option (D). Hope that helps.
Best Regards,
Ashwin (IIT Madras).
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !