Question

if the two zeroes of the polynomial are 3÷2 and 4÷3. find the polynomial​

Answer 1

Answer:

Answer: x³ - 4x² + x + 6.

Step-by-step explanation: Let the zeroes be α,β,γ. Given Zeroes are 3,2,-1. (i) Sum of its Zeroes: ⇒ α + β + γ = 3 + 2 - 1. = 4. (ii) Sum of the product taken two at a time: ⇒ αβ + βγ + γα = 3 * 2 + 2 * -1 + 3 * -1. = 1. ...

Therefore, the cubic polynomial is x³ - 4x² + x + 6. Hope it helps!

Answer 2

Step-by-step explanation:

A polynomial is given by

$k(x^{2} - (\alpha +\beta )x + \alpha \beta )\\Here, \alpha = 3/2 \\ \beta = 4/3$

Their sum = 3/2 + 4/3 = 17/6 (Taking LCM)

Their product = 3/2 x 4/3 = 2

==> The polynomial is $k(x^{2} - \frac{17}{6} x + 2)\\= \frac{1}{6} (6x^{2} - 17x + 12)\\=k(6x^{2} - 17x +12)$

Where k is any real no.

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