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CBSE Class 10 Answered

Find the product of the quadratic polynomial 3 x squared plus 5 x minus 2 Find a quadratic polynomial whose zeroes are fraction numerator 2 plus square root of 5 over denominator 2 end fractionand fraction numerator 2 minus square root of 5 over denominator 2 end fraction
Asked by kmravibhat | 20 Mar, 2019, 06:04: PM
answered-by-expert Expert Answer
I understand user wants zeros of polynomial 3x2 +5x -2

3x2 +5x -2 = 0
3x2 +6x -x -2 = 0
3x(x+2) -1(x+2) = (3x -1) (x+2) = 0
 
hence zeros of polynomial or roots of polynomial are (1/3) and -2
 
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If α and β are roots of polynomial, then the polynomial is  x2 -(α+β)x + αβ = 0
 
let α = (2+√5)/2   and  β = (2-√5)/2   hence (α+β) = 2  and   αβ = (4-5)/4 = -1/4
 
hence polynomial is x2 -2x  -(1/4) = 0  or  4x2 -8x -1 = 0
Answered by Thiyagarajan K | 20 Mar, 2019, 08:44: PM
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