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2. Find a cubic polynomial with the sum of zeroes, sum of the product of its zeroestaken two at a time and product of its zeroes as(ii) 2,-5, -20(ii)3(v) 23,CBSE SP 2011 |
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Answer» (i) Let α, β and ɣ be the roots of the cubic polynomialGiven (α + β + ɣ) = 3(αβ+ βɣ + ɣα) = – 8 and (αβɣ) = –13The cubic polynomial with roots α, β and ɣ is x³ – (α + β + ɣ)x² + (αβ+ βɣ + ɣα)x – (αβɣ) = 0⇒ x³– (3)x² + ( – 8)x – (13) = 0⇒ x³ – 3x² – 8x + 13 = 0 (ii) Let α, β and ɣ be the roots of the cubic polynomialGiven (α + β + ɣ) = 2(αβ+ βɣ + ɣα) = – 5 and (αβɣ) = –20The cubic polynomial with roots α, β and ɣ is x³ – (α + β + ɣ)x² + (αβ+ βɣ + ɣα)x – (αβɣ) = 0⇒ x³– (2)x² + ( – 5 )x – ( – 20) = 0⇒ x³ – 2x² – 5x + 20 = 0 thanks tell me 3rd part please (iii) Let α, β and ɣ be the roots of the cubic polynomialGiven (α + β + ɣ) = -4(αβ+ βɣ + ɣα) = 1/2 and (αβɣ) = –1/3The cubic polynomial with roots α, β and ɣ is x³ – (α + β + ɣ)x² + (αβ+ βɣ + ɣα)x – (αβɣ) = 0⇒ x³– (-4)x² + ( –1/2 )x – ( – 1/3) = 0⇒ 6x³ + 24x² – 3x + 2 = 0 Can we became friends and help each other on whatsapp |
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