(A) a = –7, b = –1 (B) a = 5, b = –1 (C) a = 2, b = – 6 (D) a = 0, b = – 6
(D) a = 2, b = – 6
Clarification:
As per the inquiry,
![\[x{}^\text{2}\text{ }+\text{ }\left( a+1 \right)x\text{ }+\text{ }b\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b2ff28c968069196c0a3c2703191bc9f_l3.png "Rendered by QuickLaTeX.com")
Considering that, the zeroes of the polynomial = 2 and – 3,
At the point when x = 2
![\[2{}^\text{2}\text{ }+\text{ }\left( a+1 \right)\left( 2 \right)\text{ }+\text{ }b\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-269b97d1e0966b63184b24bc453ad5ef_l3.png "Rendered by QuickLaTeX.com")
![\[4\text{ }+\text{ }2a+2\text{ }+\text{ }b\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f4a6211a07aa752bbee4518b84978b65_l3.png "Rendered by QuickLaTeX.com")
![\[6\text{ }+\text{ }2a+b\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-53fa3f1682aa64d7c1309fc7fbcdaca6_l3.png "Rendered by QuickLaTeX.com")
![\[2a+b\text{ }=\text{ }-\text{ }6\text{ }\text{ }\text{ }\left( 1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7d59f2cdfed5feae3690191f1472398d_l3.png "Rendered by QuickLaTeX.com")
At the point when x = – 3,
![\[\left( -\text{ }3 \right){}^\text{2}\text{ }+\text{ }\left( a+1 \right)\left( -\text{ }3 \right)\text{ }+\text{ }b\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e21a6b771b6573d853017f7754ed5b2b_l3.png "Rendered by QuickLaTeX.com")
![\[9\text{ }\text{ }3a-3\text{ }+\text{ }b\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f9c3bbf9ebc69a9fd2766a9543f3ca52_l3.png "Rendered by QuickLaTeX.com")
![\[6\text{ }\text{ }3a+b\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9d377d716a2f5b9ba21cc67e1fdb7019_l3.png "Rendered by QuickLaTeX.com")
![\[-\text{ }3a+b\text{ }=\text{ }-\text{ }6\text{ }\text{ }\text{ }\left( 2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-37cd6ebf8c3509e7e540206c11b7f42d_l3.png "Rendered by QuickLaTeX.com")
Deducting condition (2) from (1)
![\[2a+b\text{ }\text{ }\left( -\text{ }3a+b \right)\text{ }=\text{ }-\text{ }6-\left( -\text{ }6 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f40743da49fddc97bb1ab20f235cd0f3_l3.png "Rendered by QuickLaTeX.com")
![\[2a+b+3a-b\text{ }=\text{ }-\text{ }6+6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-625b30128036f9213db16f5390d38374_l3.png "Rendered by QuickLaTeX.com")
![\[5a\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-09cfc74d6c1d2e9c23a39922f409b7d5_l3.png "Rendered by QuickLaTeX.com")
![\[a\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e6763b6ca61e54dacae239248951a868_l3.png "Rendered by QuickLaTeX.com")
Subbing the worth of ‘a’ in condition (1), we get,
![\[2a\text{ }+\text{ }b\text{ }=\text{ }-\text{ }6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1bd10be2dfff0a073bbf492c2cb1d5a3_l3.png "Rendered by QuickLaTeX.com")
![\[2\left( 0 \right)\text{ }+b\text{ }=\text{ }-\text{ }6\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-43f62cca4ba7751e8252a7c0dacf902e_l3.png "Rendered by QuickLaTeX.com")
b = – 6
Subsequently, alternative (D) is the right reply.