If `(x^2+p x+1)` is a factor of `(a x^3+b x+c),t h e n` `a^2+c^2=-a b` b. `a^2-c^2=-a b` c. `a^2-c^2=a b` d. none of these

If x^(2)+px=1 is a factor of the expression ax^(3)+bx=c, then a^(2)-c^(2)=ab b.a^(2)+c^(2)=-ab c.a^(2)-c^(2)=-ab d.none of these

If x ^(2) +bx+b is a factor of x ^(3) +2x ^(2)+2x + c (c ne 0), then b-c is :

If x ^(2)+bx+b is a factor of x ^(3) +2x ^(2) +2x+c (c ne 0), then b-c is :

The distance of the point P(a ,\ b ,\ c) from the x-axis is a. sqrt(b^2+c^2) b. sqrt(a^2+c^2) c. sqrt(a^2+b^2) d. none of these

If f(x)=f(x)={(sin(a+1)x+sinx)/(x^x c),x<0(sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,x-0 is continuous at x=0,t h e n a=-3/2,b=0,c=1/2 (b) a=-3/2,b=1,c=-1/2 a=-3/2,b in R-[0],c=1/2 (d) none of these

If (x-2) is a common factor of the expressions x^(2)+ax+b and x^(2)+cx+d , then (b-d)/(c-a)

If sinalpha and cosalpha are the roots of the equation a x^2+b x+c=0 , then b^2= a^2-2a c (b) a^2+2a c (c) a^2-a c (d) a^2+a c

If a, b, c are real and x^3-3b^2x+2c^3 is divisible by x -a and x - b, then (a) a =-b=-c (c) a = b = c or a =-2b-_ 2c (b) a = 2b = 2c (d) none of these

If x-a is a factor of x^(3)-3x^(2)a+2a^(2)x+b then the value of b is 0(b)2(c)1(d)3