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polynomial

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If one zero of the polynomial 3x^2 + 12x - k is reciprocal of the other , then find the value of k. ​

Jun 20, 2022

#1
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By Vieta's formula, $$\text{product of roots} = \dfrac{-k}3$$.

But since one zero is the reciprocal of the other, product of roots is 1.

Therefore, $$\dfrac{-k}3 = 1$$. That means k = -3.

Jun 20, 2022