Question

Assertion (A)
A monic quadratic polynomial having 4 and −2 as zeroes is x² − 2x − 8.

Reason (R)
The monic quadratic polynomial having α and β as zeroes is given by p(x) = x² − (α + β) x + αβ.

(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

$$\begin{gathered} \left(\mathrm{a}\right)\mathrm{Both}\mathrm{the}\mathrm{assertion}\left(\mathrm{A}\right)\mathrm{and}\mathrm{reason}\left(\mathrm{R}\right)\mathrm{are}\mathrm{true}\mathrm{and}\mathrm{reason}\left(\mathrm{R}\right)\mathrm{is}\mathrm{a}\mathrm{correct}\mathrm{explanation}\mathrm{of}\left(\mathrm{A}\right). \\ \text{Let}\alpha \text{=4 and}\beta =-2. \\ \text{Then}\alpha \text{+}\beta \text{=2 and}\alpha \beta \text{=}-8 \\ \therefore \mathrm{Required}\mathrm{polynomial}=x^2-(\mathrm{\alpha }+\mathrm{\beta })x+\mathrm{\alpha \beta }=x^2-2x-8 \\ \mathrm{i}.\mathrm{e}.,\mathrm{a}\text{ssertion}\left(\text{A}\right)\text{is true}\text{.} \end{gathered}$$