If `b^(2) lt 2ac`, the equation `ax^(3)+bx^(2)+cx+d=0` has (where a, b, c, d in R and `a gt 0`)

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

Discuss the nature of roots of equation x^(2) +ax +b =0 and x^(2) +cx + d=0, where a,b,c, d are real numbers and ac = 2( b +d)

Discuss the nature of roots of equation x^(2) +ax +b =0 and x^(2) +cx + d=0, where a,b,c, d are real numbers and ac = 2( b +d)

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

If one root of the equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0, (a, b, c in R) is common, then the value of ((a^(3)+b^(3)+c^(3))/(abc))^(3) is

If the roots of the equation x^(3) + bx^(2) + cx + d = 0 are in arithmetic progression, then b, c and d satisfy the relation

If the roots of the equation x^(3) + bx^(2) + cx + d = 0 are in arithmetic progression, then b, c and d satisfy the relation

If a, b , c in R and 3b^(2)-8ac lt 0 , then the equation ax^(4)+bx^(3)+cx^(2)+5x-7=0 has a) all real roots b) all imaginary roots c)exactly two real and two imaginary roots d) none

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