\(4{x^3} + 12{x^2} - 15x + 4 = 0\) has a root of multiplicity of \(2\). The root is?

\({x^4} + 2{x^3} - 12{x^2} + 14x - 5 = 0\) has a root of multiplicity of \(3\). The root is?

\(P(x) = {x^3} - 6{x^2} + 9x + k\) has a root of multiplicity of \(2\). A possible value of \(k\) is?

\(P(x) = {x^4} + a{x^3} + b{x^2} + cx - 16\) has a triple root at \(x = 2\). The values of \(a\), \(b\) and \(c\) are?

Solve the equation \(2{x^3} - 15{x^2} + 24x + 16 = 0\) given that it has a double root.

Solve the equation \({x^4} + 2{x^3} - 12{x^2} + 14x - 5 = 0\) given that it has a triple root.

Find the values of \(p\) and \(q\) given that \(P(x) = 2{x^3} - (2p + 1){x^2} + (2 + q)x - 1\) has double root at \(x = 1\).

\(P(x) = {x^4} - 3{x^3} - 6{x^2} + 28x - 24\) has a triple zero, find all the zeros of \(P(x)\).

The polynomial \(P(x)=x^3-6 x^2+9 x+k\) has a double root. Find the two possible values for \(k\) and all the roots for each value of \(k\).

The polynomial \(P(x)=x^3+3 x^2-24 x+k\) has a double root. Find the two possible values of \(k\) and all the roots.

Find the real roots of \(P(x)=x^3-7 x^2+11 x-5\) given that \(P(x)\) has a double root.

The line \(y=4 x-5\) is a tangent to the curve \(y=x^3-2 x^2+3\) at the point \((2,3)\). The tangent meets the curve again at \(Q\).

Find the coordinates of \(Q\).

If \(P(x)=x^3-3 x^2+4\), show that \(P(x)\) has a multiple zero and find the zero and its multiplicity.

If \(p x^3+q x^2+r=0\) has a double root, show that \(27 p^2 r+4 q^3=0\).