If f and g are polynomials of degrees m and n respectively, and if h(x) = (f ^_o g)(x), then the degree of h is

A polynomial equation in x of degree n always has

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 \((2+\sqrt{3})^{x^{2}-2 x+1}+(2-\sqrt{3})^{x^{2}-2 x-1}=\frac{2}{2-\sqrt{3}}\) then x = _________

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

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

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

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. \(a \neq 0\)

Form a polynomial equation with integer coefficients with \(\sqrt { \frac { \sqrt { 2 } }{ \sqrt { 3 } } } \) as a root.

Find the number of real solutions of sin (e^x) -5^x + 5^-x

Solve: 2x+2^x-1+2^x-2 = 7x+7^x-1+7^x-2

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

Form the equation whose roots are the squares of the roots of the cubic equation x³+ ax²+ bx + c = 0.

Find a polynomial equation of minimum degree with rational coefficients, having \(\sqrt{5}\)−\(\sqrt{3}\) as a root.

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.