Let `f(x)=a x^2+b x+cdot` Consider the following diagram. Then Fig `c<0` `b >0` `a+b-c >0` `a b c<0`

Let f(X) = ax^(2) + bx + c . Consider the following diagram .

Let the parabolas y=x(c-x) and y=x^(2)+ax+b touch each other at the point (1,0). Then a+b+c=0a+b=2b-c=1(d)a+c=-2

L_1=(a-b)x+(b-c)y+(c-a)=0L_2=(b-c)x+(c-a)y+(a-b)=0L_3=(c-a)x+(a-b)y+(b-c)=0 KAMPLE 6 Show that the following lines are concurrent L1 = (a-b) x + (b-c)y + (c-a) = 0 12 = (b-c)x + (c-a) y + (a-b) = 0 L3 = (c-a)x + (a-b) y + (b-c) = 0. ,

Let f(x)=x^(2)-bx+c, b is a odd positive integer,f(x)=0 have two prime numbers as roots and b+c=35 Then the global minimum value of f(x) is

Let f(x)=a+b|x|+c|x|^(2) , where a,b,c are real constants. The, f'(0) exists if

Let a ,b ,c in Q^+ satisfying a > b > cdot Which of the following statements (s) hold true of the quadratic polynomial f(x)=(a+b-2c)x^2+(b+c-2a)x+(c+a-2b)? The mouth of the parabola y=f(x) opens upwards Both roots of the equation f(x)=0 are rational The x-coordinate of vertex of the graph is positive The product of the roots is always negative

Let f(x)=ax^(2)-bx+c^(2)!=0 and f(x)!=0 for all x in R. Then (a)a^(2)+c^(2)2(b)c(c)a-3b+c^(2)<0 (d) non of these

Evaluate the following limit : (lim)_(x->0)((a^x+b^x+c^x)/3),\ (a , b ,\ c >0)