A zero of x³ + 64 is

The number of real numbers in [0, 2π] satisfying sin⁴x - 2sin²x + 1 is

The number of positive zeros of the polynomial \(\overset { n }{ \underset { j=0 }{ \Sigma } } { n }_{ C_{ r } }\)(-1)^rx^r is

For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has ________

If x² - hx - 21 = 0 and x² - 3hx + 35 = 0 (h > 0) have a common root, then h = ___________

If α, β, and γ are the roots of the equation x³ + px² + qx + r = 0, find the value of  \(\Sigma \frac { 1 }{ \beta \gamma } \) in terms of the coefficients.

Find the monic polynomial equation of minimum degree with real coefficients having 2 -\(\sqrt{3}\)i as a root.

If x²+2(k+2)x+9k = 0 has equal roots, find k.

Solve the equation : x⁴-14x² + 45 = 0

Examine for the rational roots of x⁸- 3x + 1 = 0

If α and β are the roots of the quadratic equation 2x²−7x+13 = 0 , construct a quadratic equation whose roots are α² and β².

Find the sum of squares of roots of the equation 2x⁴- 8x³+ 6x²-3 = 0.

If α, β, and γ are the roots of the polynomial equation ax³+ bx²+ cx + d = 0, find the value of \(\Sigma \frac { \alpha }{ \beta \gamma } \) in terms of the coefficients.

Solve the equation x⁴-9x²+20 = 0.

Solve the equation x³- 5x²- 4x + 20 = 0

Solve the equation 3x³ - 16x² + 23x - 6 = 0 if the product of two roots is 1.

Solve the equation (x-2) (x-7) (x-3) (x+2)+19 = 0

Solve: (x - 4)(x - 7)(x - 2)(x + 1) = 16