Let `f(x)=a x^2+b x+cw h e ra in R^+a n db^2-4a c<0.` Area bounded by `y=f(x),` x-axis and the lines `x=0,x=1` is equal to `1/6(3f(1)+f(-1)+2f(0))` b. `1/(12)(5f(1)+f(-1)+8f(0))` c. `1/6(3f(1)-f(-1)+2f(0))` d. `1/(12)(5f(1)-f(-1)+8f(0))`

Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5)=-3f(2) and that 3 is a root of f(x)=0. Then find the other of f(x)=0.

Let P(x)=x^2+b x+cw h e r eba n dc are integer. If P(x) is a factor of both x^4+6x^2+25a n d3x^4+4x^2+28 x+5,t h e n a. P(x)=0 has imaginary roots b. P(x)=0 has roots of opposite c. P(1)=4 d . P(1)=6

Let f(x)=x^2+b x+c ,w h e r eb ,c in Rdot If f(x) is a factor of both x^4+6x^2+25a n d3x^4+4x^4+28 x+5 , then the least value of f(x) is 2 b. 3 c. 5//2 d. 4

Let f(x)=x^2+b x+c ,w h e r eb ,c in Rdot If f(x) is a factor of both x^4+6x^2+25 and 3x^4+4x^2+28 x+5 , then the least value of f(x) is: (a.) 2 (b.) 3 (c.) 5//2 (d.) 4

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if f(x) is an integer whenever x is an integer, then the numbers 2A ,A+B ,a n dC are all integer. Conversely, prove that if the number 2A ,A+B ,a n dC are all integers, then f(x) is an integer whenever x is integer.

Suppose f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db are positive integers. If f(g(20))-g(f(20))=28 , then which of the following is not true? a=15 b. a=6 c. b=14 d. b=3

Let f : R rarr R be defined by f(x) = x^(2) - 3x + 4 for all x in R , then f (2) is equal to

Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in R. Also given that f (x) =0 has no real roots and 4a + b gt 0. Let p =b-4a, q=2a +b, then pq is:

Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R . Then (a) a+c^2 2b (c) a-3b+c^2 < 0 (d) none of these