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

Find the roots of the equation 2x^2 - x + 1/8 = 0

Find the condition that the equation x^3 - px^2 + qx -x = 0 should have its roots in G.P.

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

Find the condition if equations ax^2+bx+c =0 and x^2+2x+3 =0 have a common root. (a,b,cinR)

Find the roots of the equation x+(1)/(x)=3, x ne 0

Find the condition for which the quadratic equation ax^2+bx+c=0 has exactly one zero root.

Find the root of equation 2x^2+3 x + 11=0.

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.

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 -