According to the rational root theorem, which number is not possible rational zero of 4x⁷ + 2x⁴ - 10x³ - 5?

The polynomial x³ - kx² + 9x has three real zeros if and only if, k satisfies

Let a > 0, b > 0, c >0. Theh n both the root of the equation ax²+bx+c = 0 are _________

The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has ____________

If the equation ax²+ bx+c = 0(a > 0) has two roots ∝ and β such that ∝ <- 2 and β > 2, then __________

1) \(x+\frac { 1 }{ x } =2\)
2) ax² + bx + c = 0
3) \(\sqrt { x } +\frac { 1 }{ \sqrt { x } } =4\)
4) \({ ax }^{ 2 }+\frac { b }{ x } +c=0\)

If ax + by = 1, cx² + dy² = 1 have only one solution, then
(1) \(\frac { { a }^{ 2 } }{ c } +\frac { { b }^{ 2 } }{ d } =1\)
(2) \(x=\frac { a }{ c } \)
(3) \(x=\frac { c }{ a } \)
(4) \(x=\frac { b }{ d } \)

Find a polynomial equation of minimum degree with rational coefficients, having 2-\(\sqrt{3}\) as a root.

Show that the equation 2x²− 6x +7 = 0 cannot be satisfied by any real values of x.

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

Find the sum of the squares of the roots of ax⁴+ bx³+ cx²+ dx + e = 0. \(a \neq 0\)

If α, β and γ are the roots of the cubic equation x³+ 2x²+ 3x + 4 = 0, form a cubic equation whose roots are \(\frac { 1 }{ \alpha } ,\frac { 1 }{ \beta } ,\frac { 1 }{ \gamma } \)

Find the number of positive integral solutions of (pairs of positive integers satisfying) x² - y² = 353702.

If 2+i and 3-\(\sqrt{2}\) are roots of the equation x⁶-13x⁵+ 62x⁴-126x³+ 65x²+127x-140 = 0, find all roots.

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

If the sum of the roots of the quadratic equation ax²+ bx + c = 0 (abc ≠ 0)  is equal to the sum of the squares of their reciprocals, then \(\frac { a }{ c } ,\frac { b }{ a } ,\frac { c }{ b } \)  are H.P.