Mahabir Singh Solutions for Chapter: Quadratic Equations, Exercise 3: ACHIEVERS SECTION (HOTS)

Which of the following equations has two distinct real roots?

Read the statement carefully and state ‘T’ for true and ‘F’ for false.
(i) The value of $2+\frac{1}{2+\frac{1}{2+\dots \mathrm{\infty }}}$ is $\sqrt{2}$.
(ii) A line segment $\mathrm{AB}$ of length $2\mathrm{m}$ is divided at $\mathrm{C}$ into two parts such that ${\mathrm{AC}}^2=\mathrm{AB}\bullet \mathrm{CB}.$ The length of the part $\mathrm{CB}$ is $3+\sqrt{5}$.
(iii) Every quadratic equation can have at most two real roots.
(iv) A real number $\alpha$ is said to be the root of the quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,$ if ${\mathrm{a\alpha }}^2+\mathrm{b\alpha }+\mathrm{c}=0$.

The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is $2\frac{16}{21}$, find the fraction.