If `(12a+5b)/(15)=-((c+d))/(4),` then the equation `ax^(4)+bx^(2)+cx+d=0` has

If a,b,c,d are real numbers such that (3a+2b)/(c+d)+(3)/(2)=0 then the equation ax^(3)+bx^(2)+cx+d=0 has

If a,b,c d in R such that (a+2c)/(b+3d) +4/3=0, then the equation ax ^(3) + bx^(3)+ cx+d =0 has

If a, b, c, d are real numbers such that (a+2c)/(b+3d)+(4)/(3)=0 . Prove that the equation ax^(3)+bx^(2)+cx+d=0 has atleast one real root in (0, 1).

If 27a+9b+3c+d=0 then the equation 4ax^(3)+3bx^(2)+2cx+d has at leat one real root lying between

If (1)/(2),(1)/(3),(1)/(4) are the roots of ax^(3)+bx^(2)+cx+d=0 then the roots of a(x+1)^(3)+b(x+1)^(2)+c(x+1)+d=0 are

If 1,2,3 and 4 are the roots of the equation x^(4)+ax^(3)+bx^(2)+cx+d=0, then a+2b+c=

If (1)/(2),(1)/(3),(1)/(4) are the roots of ax^(3)+bx^(3)+cx+d=0 then the roots of a(x+1)^(3)+b(x+1)^(2)+c(x+1)+d=0 are

Let a, b and c be real numbers such that 4a + 2b + c = 0 and ab gt 0. Then the equation ax^(2) + bx + c = 0 has