If the sum of the zeroes of the polynomial p(x) = (a + 1)x2 + (2x + 3)

1.	If the sum of the zeroes of the polynomial p(x) = (a + 1)x2 + (2x + 3)x + (3x + 4) is -1, find the product of the zeroes.
Answer» P(x) = (a + 1)x² + (2x + 3)x + (3x + 4) = (a + 3)x² + 6x + 4 Sum of zeros = -1 (Given) ⇒ \(\frac{-6}{a + 3} = -1\) ⇒ a + 3 = 6 ⇒ a = 6 - 3 = 3 ∴ Product of zeroes = \(\frac{4}{a + 3} = \frac{4 }{3 +3} = \frac46 = \frac23\).

If the sum of the zeroes of the polynomial p(x) = (a + 1)x2 + (2x + 3)x + (3x + 4) is -1, find the product of the zeroes.

Answer»

P(x) = (a + 1)x² + (2x + 3)x + (3x + 4)

= (a + 3)x² + 6x + 4

Sum of zeros = -1 (Given)

⇒ \(\frac{-6}{a + 3} = -1\)

⇒ a + 3 = 6

⇒ a = 6 - 3 = 3

∴ Product of zeroes = \(\frac{4}{a + 3} = \frac{4 }{3 +3} = \frac46 = \frac23\).

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If the sum of the zeroes of the polynomial p(x) = (a + 1)x2 + (2x + 3)x + (3x + 4) is -1, find the product of the zeroes.

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