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

The equation sin x+x cos x=0 has at least one root in

Find the roots of the equation 3x^(2)+2x=0

Statement-1: If a, b, c in R and 2a + 3b + 6c = 0 , then the equation ax^(2) + bx + c = 0 has at least one real root in (0, 1). Statement-2: If f(x) is a polynomial which assumes both positive and negative values, then it has at least one real root.

If a+b + c = 0, then show that the quadratic equation 3ax^(2) + 2bx +c=0 has at least one root in [0,1].

Statement I The equation 3x^(2)+4ax+b=0 has atleast one root in (o,1), if 3+4a=0. Statement II f(x)=3x^(2)+4x+b is continuos and differentiable in (0,1)

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

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.

If a+b+2c=0, c!=0, then equation ax^2+bx+c=0 has (A) at least one root in (0,1) (B) at least one root in (0,2) (C) at least on root in (-1,1) (D) none of these

Find the range of values of 'a' so that the equation x^(2)-(a-5)x+(a-(15)/(4))=0 has at least one positive root