Question

Assertion (A)
The polynomial p(x) = x³ + x has one real zero.

Reason (R)
A polynomial of nth degree has at most n zeros.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Answer 1

$$\begin{gathered} \left(\mathrm{b}\right)\mathrm{Both}\mathrm{Assertion}\left(\mathrm{A}\right)\mathrm{and}\mathrm{Reason}\left(\mathrm{R}\right)\mathrm{are}\mathrm{true}\mathrm{but}\mathrm{Reason}\left(\mathrm{R}\right)\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{correct}\mathrm{explanation}\mathrm{of}\mathrm{Assertion}\left(\mathrm{A}\right). \\ p\left(x\right)=0 \\ =>(x^3+x)=0 \\ =>x(x^2+1)=0 \\ =>x=0\text{or}{x}^2+1=0 \\ \text{But}{x}^2+1\ne 0,\text{for any real value of}x.[\because x^2+1>0] \\ \therefore p\left(x\right)\text{has one real zero, i}\text{.e}\text{., 0}\text{.} \\ \therefore \text{Asseration}\left(\text{A}\right)\text{is true and reason}\left(\text{R}\right)\text{does not clearly explain Assertion}\left(\text{A}\right). \end{gathered}$$