13) If one zero of the polynomial $(a^{2} + 9) x - 3 a x + 4 a^{2}$ is reciprocal if other. Find the value of a.

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Solution

Dear Student,

$L e t t h e' z' b e t h e z e r o o f t h e p o l y n o m i a l a n d o t h e r o n e w i l l b e \frac{1}{z} N o w, P r o d u c t o f t h e z e r o = \frac{C o n s \tan t t e r m}{C o e f f i c i e n t o f t h e x^{2}} z \times \frac{1}{z} = \frac{4 a^{2}}{(a^{2} + 9)} 1 = \frac{4 a^{2}}{(a^{2} + 9)} a^{2} + 9 = 4 a^{2} 3 a^{2} - 9 = 0 a^{2} - 3 a^{2} = 3 a = 3 o r - 3$

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