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प्रश्न
Find a cubic polynomial whose zeroes are `1/2`, 1 and –3.
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उत्तर
If the zeroes of the cubic polynomial are a, b and c then the cubic polynomial can be found as
x3 – (a + b + c)x2 + (ab + bc + ca)x – abc ...(1)
Let a = `1/2`, b = 1 and c = –3
Substituting the values in (1), we get
`x^3 - (1/2 + 1 - 3)x^2 + (1/2 - 3 - 3/2)x - (-3/2)`
⇒ `x^3 - (-3/2)x^2 - 4x + 3/2`
⇒ 2x3 + 3x2 – 8x + 3
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