If `b^2>4a c` then roots of equation `a x^4+b x^2+c=0` are all real and distinct if: `b<0,a<<0,>>0` (b) `b<<0,a>>0,c >0` `b >0,a >0,c >0` (d) `b >0,a<0,c<0`

The roots of the equation 2a^(2)x^(2) - 2abx + b^(2) = 0 when a lt 0 and b gt 0 are :

Figure 2.23 shows the graph of the polynomial f(x)=a x^2+b x+c for which (FIGURE) (a) a<<0, b>>0 a n d c >0 (b) a<0, blt0 and cgt0 (c) a<0, b<0 a n d c<0 (d) a >0, b >0 a n d c<0

If a gt 0, b gt 0 and c gt 0 , then both the roots of the equations ax^2 + bx + c =0

Figure 2.23 shows the graph of the polynomial f(x)=a x^2+b x+c for which (FIGURE) (a) a<<0,\ \ b>>0\ a n d\ c >0 (b) a<0, blt0 and cgt0 (c) a<0,\ b<0\ a n d\ c<0 (d) a >0,\ b >0\ a n d\ c<0

Let a gt 0, b gt 0, c gt 0 . Then both the roots of the equation ax^2+ bx + c = 0 are

The roots of the equation ax^2+bx + c = 0 will be imaginary if, A) a gt 0 b=0 c lt 0 B) a gt 0 b =0 c gt 0 (C) a=0 b gt 0 c gt 0 (D) a gt 0, b gt 0 c =0

The direction ratios of a normal to the plane through (1,0,0)a n d(0,1,0) , which makes and angle of pi/4 with the plane x+y=3, are a. <<1,sqrt(2),1 >> b. <<1,1,sqrt(2)>> c. <<1,1,2>> d. << sqrt(2),1,1>>

The direction ratios of a normal to the plane through (1,0,0)a n d(0,1,0) , which makes and angle of pi/4 with the plane x+y=3, are a. <<1,sqrt(2),1 >> b. <<1,1,sqrt(2)>> c. <<1,1,2>> d. << sqrt(2),1,1>>