If α And β Are the Zeros of the Quadratic Polynomial P(Y) = 5y2 − 7y + 1, Find the Value of 1/Alpha+1/Beta - Mathematics

If α and β are the zeros of the quadratic polynomial p(y) = 5y2 − 7y + 1, find the value of 1/alpha+1/beta

Solution

Since 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the polynomials

p(y) = 5y2 – 7y + 1

Sum of the zeroes alpha+beta="-coeeficient of x"/("coefficient of "x^2)

=-(-7)/5

=7/5

Product of zeroes =alphabeta="constant term"/"coefficient of "x^2

=1/5

We have, 1/alpha+1/beta=(alpha+beta)/(alphabeta)

By substituting alpha+beta=7/5 and alphabeta=1/5 we get,

1/alpha+1/beta=(7/5)/(1/5)

1/alpha+1/beta=7/5xx5/1

1/alpha+1/beta=7

Hence, the value of 1/alpha+1/beta is 7

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 2 Polynomials
Exercise 2.1 | Q 9 | Page 34