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

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

If x is real and \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then ________

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

If ∝, β, ૪ are the roots of the equation x³-3x+11 = 0, then ∝+β+૪ is __________.

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.

Show that the equation x⁹- 5x⁵+ 4x⁴+ 2x²+ 1 = 0 has atleast 6 imaginary solutions.

Find value of a for which the sum of the squares of the equation x² - (a- 2) x - a -1 = 0 assumes the least value.

Find x If \(x=\sqrt { 2+\sqrt { 2+\sqrt { 2+....+upto\infty } } } \)

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

Find the condition that the roots of cubic x³+ ax²+ bx + c = 0 are in the ratio p : q : r.

Solve the equation 9x³- 36x²+ 44x -16 = 0 if the roots form an arithmetic progression.

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

Solve: \({ (5+2\sqrt { 6 } ) }^{ { x }^{ 2 }-3 }+{ (5-2\sqrt { 6 } ) }^{ { x }^{ 2 }-3 }=10\)

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

Solve the equation (2x-3) (6x-1) (3x-2) (x-2)-5 = 0

If a, b, c, d and p are distinct non-zero real numbers such that (a²+b²+c²) p²-2 (ab+bc+cd) p+(b²+c²+d²)≤ 0 then prove that a, b, c, d are in G.P and ad = bc

Solve: (2x² - 3x + 1) (2x² + 5x + 1) = 9x².