Q. 134.7( 18 Votes )

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Answer :

To Find: a and b


Concept Used:


If k is a root of a polynomial f(x), then f(k) = 0


Explanation:


Let f(x) = ax2 + 7x + b = 0


Now,




4a + 42 + 9b = 0


4a + 9b = –42 …..(1)


f(–3) = = a(–3)2 + 7(–3) + b = 0


9a + b – 21 = 0


9a + b = 21….(2)


Multiplying equation (2) by 9, we get,


81a + 9b = 189….(3)


Subtracting equation (1) from equation (3), we get,


81a – 4a + 9b – 9b = 189 – (–42)


77a = 231


a = 3


Putting the value of a in equation 1, we get,


4 × 3 + 9b = –42


12 + 9b = –42


9b = –54


b = –6


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