If $$\alpha<1$$ be a root of the equation $$2 x^2-5 x+2=0$$, then the other root of the equation is

Let $$\alpha, \beta$$ be the roots of the equation $$x^2-p x+r=0$$ and $$\frac{\alpha}{2}, 2 \beta$$ be the roots of the equation $$x^2-q x+r=0$$. Then, the value of $$r$$ is equal to

If $$\alpha$$ be a root of the equation $$4{x^2} + 2x - 1 = 0$$, then the other root of the equation is

Let a, b be the solutions of x² + px + 1 = 0 and c, d be the solution of x² + qx + 1 = 0. If (a $$-$$ c) (b $$-$$ c) and (a + d)(b + d) are the solution of x² + ax + $$\beta$$ = 0, then $$\beta$$ is equal to

If a$$\in$$R, b$$\in$$R, then the equation x² $$-$$ abx $$-$$ a² = 0 has

The solution of the inequality $${4^{ - x + 0.5}} - {7.2^{ - x}} < 4$$, x $$\in$$R is

Let x₁ and x₂ be the real roots of the equation $${x^2} - (k - 2)x + ({k^2} + 3k + 5) = 0$$, then maximum value of $$x_1^2 + x_2^2$$ is

When x¹⁰⁰ is divided by x² $$-$$ 3x + 2, the remainder is (2^{k + 1} $$-$$ 1)x $$-$$(2^k $$-$$ 1), then k is