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CBSE Class 10 Answered

If αand βare the two zero polynomial  of the polynomial x ²-3x+2 find quadratic polynomial whose zeros are α+βand 1/α+1/β  
Asked by kamleshmishra.3005 | 28 May, 2019, 23:10: PM
answered-by-expert Expert Answer
 
Here α and β are the two zero polynomial of the polynomial x² - 3x + 2. 
a= 1, b = -3 and c = 2
 
α + β = -b/a = -(-3)/1 = 3
αβ = c/a = 2/1 = 2
 
So we have α + β = 3 and 1/α  + 1/β = α + β/αβ = 3/2  ... (i)
 
We know that,
x2  - (sum of the zeros)x + product of the zeroes
= x2  - (3 + 3/2) + (3 × 3/2) ... from (i)
= x2  - 9/2x + 9/2  ... is the required polynomial
Answered by Yasmeen Khan | 29 May, 2019, 09:59: AM

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