For which values of 'a' so that the equation `x^(2)+(3-2a)x+a=0` has exactly one root in the interval `(-1,2)`

Find the value of l'al'so that the equation f(x)=x^(2)+(a-3)x+a=0 has exactly one alpha between the interval (1,2) and f(x+alpha)=0 has exactly one root between the interval (0,1)

Find the value of l'al'so that the equation f(x)=x^(2)+(a-3)x+a=0 has exactly one alpha between the interval (1,2) and f(x+alpha)=0 has exactly one root between the interval (0,1)

Prove that the equation x^3 + 2x^2 +x + 4 = 0 has exactly one root in the open interval (-3,-2).

Prove that the equation x^(3) + x – 1 = 0 has exactly one real root.

Consider the expression g(x)=sin^(2)x-(b+1)sin x+3(b-2) where b is a real parameter Number of integral values of b for which the equation g(x)=0 has exactly one root in the interval (0,pi) are

For what vlaue of a do the equations x^(2)+ax+1=0 and x^(2)+x+a=0 have exactly one root in common

Find the value of k so that the equation 2x^(2)-5x+k=0 has two equal roots.

Let- 1<=p<1 show that the equation 4x^(3)-3x-p=0 has a unique root in the interval [(1)/(2),1]

Find the values of k so that the quadratic equation 2x^(2)-(k-2)x+1=0 has equal roots

The value of k so that the equation x^(3)-12x+k=0 has distinct roots in [0,2] is