If `3(a+2c)=4(b+3d),` then the equation `a x^3+b x^2+c x+d=0` will have a.no real solution b.at least one real root in `(-1,0)` c.at least one real root in `(0,1)` b.none of these

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

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

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^2+2bx+c=0 has (a) at least one root in [0, 1] (b) at least one root in [1,2] (c) at least one root in [3/2, 2] (d) none of these

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a) 6 real roots b) at least 2 real roots c) 4 real roots d) none of these

Let a ,b , c in R such that no two of them are equal and satisfy |(2a, b, c),( b, c,2a), (c, 2a, b)|=0, then equation 24 a x^2+8b x+4c=0 has (a) at least one root in [0,1] (b) at least one root in [-1/2,1/2] (c) at least one root in [-1,0] (d) at least two roots in [0,2]

If 2a+3b+6c=0 " "(a, b, c in R) , then the quadratic equation ax^(2)+bx+c=0 has at least one root -

If the equation a x^2+b x+c=0 has two positive and real roots, then prove that the equation a x^2+(b+6a)x+(c+3b)=0 has at least one positive real root.

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.