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

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

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

If a,b,c are real distinct numbers such that a ^(3) +b ^(3) +c ^(3)= 3abc, then the quadratic equation ax ^(2) +bx +c =0 has (a) Real roots (b) At least one negative root (c) Both roots are negative (d) Non real roots

Prove that the equation x^2(a^2+b^2)+2x(a c+b d)+(c^2+d^2)=0 has no real root, if a d!=b c .

Prove that the equation x^2(a^2+b^2)+2x(a c+b d)+(c^2+d^2)=0 has no real root, if a d!=bc dot

If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one real lying in the interval