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+1 vote
1.3k views
in Polynomials by (32.2k points)
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If the sum of the zeroes of the quadratic polynomial kx2 + 2x + 3k is equal to the product of its zeroes, then k = ?

(a) \(\frac{1}3\)

(b) \(\frac{-1}3\)

(c) \(\frac{2}3\)

(d) \(\frac{-2}3\)

1 Answer

+2 votes
by (32.1k points)
selected by
 
Best answer

(d) \(\frac{-2}3\) 

Let α and β be the zeroes of kx2 + 2x + 3k. 

Then α + β = \(\frac{-2}k\) and αβ = 3

⇒ α + β = αβ

⇒ \(\frac{-2}k\) = 3

⇒ k = \(\frac{-2}3\)

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