Home
Class 11
MATHS
Let f(x)=ax^(2)+bx+c,if a>0 then f(x) ha...

Let `f(x)=ax^(2)+bx+c,`if `a>0` then `f(x)` has minimum value at x=

A

9

B

10

C

11

D

12

Text Solution

Verified by Experts

Given that `AC=4sqrt(2)` units
`:.AB=BC=(AC)/(sqrt(2))=4` units andd `OB=sqrt((BC)^(2)-(OC)^(2))`
`=sqrt((4)^(2)-(2sqrt(2))^(2))[ :' OC=(AC)/2]`
`=2sqrt(2)` units
`:.` Vertices are `A=(-2sqrt(2),0)`,
`B=-(0,-2sqrt(2))`
and `C=(2sqrt(2),0)`
`f(x)=0`
`implies(x^(2))/(2sqrt(2))-2sqrt(2)=0impliesx=+-2sqrt(2)`
Given `-2sqrt(2) lt (lamda)/2lg2sqrt(2)`
or `-4sqrt(2)lt lamda lt 4sqrt(2)`
`:.` Initial values of `lamda` are ,brgt `-5,-4,-3,-2,-1,0,1,2,3,4,5`
`:.` Number of integral values is 11.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)=(x-2)^2x^n, n in N Then f(x) has a minimum at

Let f(x)=x^(2)+ax+b. If the maximum and the minimum values of f(x) are 3 and 2 respectively for 0<=x<=2, then the possible ordered pairs) of (a,b) is/are

Consider the polynomial f(x)=ax^(2)+bx+c. If f(0),f(2)=2 then the minimum value of int_(0)^(2)|f'(x)dx is

Let f(x)=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f (x). As b varies, the range of m (b) is

Let f(x0=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

A polynomial function f(x) is such that f''(4)= f''(4)=0 and f(x) has minimum value 10 at ax=4 .Then

Let f(x)=ax^(2)+bx+a,b,c in R. If f(x) takes real values for real values of x and non- real values for non-real values of x ,then a=0 b.b=0 c.c=0 d.nothing can be said about a,b,c.