1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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.

Open in App
Solution

## $\left(\mathrm{a}\right)\mathrm{Both}\mathrm{the}\mathrm{assertion}\left(\mathrm{A}\right)\mathrm{and}\mathrm{reason}\left(\mathrm{R}\right)\mathrm{are}\mathrm{true}\mathrm{and}\mathrm{reason}\left(\mathrm{R}\right)\mathrm{is}\mathrm{a}\mathrm{correct}\mathrm{explanation}\mathrm{of}\left(\mathrm{A}\right).\phantom{\rule{0ex}{0ex}}\text{Let}\alpha \text{=4 and}\beta =-2.\phantom{\rule{0ex}{0ex}}\text{Then}\alpha \text{+}\beta \text{=2 and}\alpha \beta \text{=}-8\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Required}\mathrm{polynomial}={x}^{2}-\left(\mathrm{\alpha }+\mathrm{\beta }\right)x+\mathrm{\alpha \beta }={x}^{2}-2x-8\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.,\mathrm{a}\text{ssertion}\left(\text{A}\right)\text{is true}\text{.}$

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Introduction
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program