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# If α And β Are the Zeros of the Quadratic Polynomial P(S) = 3s2 − 6s + 4, Find the Value of Alpha/Beta+Beta/Alpha+2[1/Alpha+1/Beta]+3alphabeta - CBSE Class 10 - Mathematics

ConceptRelationship Between Zeroes and Coefficients of a Polynomial

#### Question

If α and β are the zeros of the quadratic polynomial p(s) = 3s2 − 6s + 4, find the value of alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta

#### Solution

Since α and β are the zeros of the quadratic polynomial p(s) = 3s2 − 6s + 4

alpha+beta="-coefficient of x"/("coefficient of "x^2)

alpha+beta=(-(-6))/3

alpha+beta=6/3

alpha+beta=2

alphabeta="constant term"/("coefficient of "x^2)

alphabeta=4/3

We have, alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta

=(alpha^2+beta^2)/(alphabeta)+2[1/alpha+1/beta+3alphabeta]

=((alpha+beta)^2-2alphabeta)/(alphabeta)+2[(alpha+beta)/(alphabeta)]+3alphabeta

By substituting alpha+beta=2 " and "alphabeta=4/3 we get,

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=((2)^2-2(4/3))/(4/3)+2((2))/(4/3)+3(4/3)

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=(4-8/3)/(4/3)+4/(4/3)+12/3

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=((4xx3)/(1xx3)-8/3)/(4/3)+4/(4/3)+12/3

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=((12-8)/3)/(4/3)+4/(4/3)+12/3

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=(4/3)/(4/3)+4/(4/3)+12/3

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=4/3xx3/4+(4xx3)/4+12/3

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=1+12/4+12/3

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=(1xx12)/(1xx12)+(12xx3)/(4xx3)+(12xx4)/(3xx4)

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=(12+36+48)/12

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=(48+48)/12

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=96/12

alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta=8

Hence, the value of alpha/beta+beta/alpha+2[1/alpha+1/beta]+3alphabeta " is "8

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#### APPEARS IN

RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 2: Polynomials
Ex. 2.10 | Q: 10 | Page no. 34

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Solution If α And β Are the Zeros of the Quadratic Polynomial P(S) = 3s2 − 6s + 4, Find the Value of Alpha/Beta+Beta/Alpha+2[1/Alpha+1/Beta]+3alphabeta Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
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