1.

If α and β are the zeros of x^2 – (5 + 7k)x + 35k, such that α^2 + β^2 = 172 is then the value of k is _______(a) 6√3(b) √3(c) 3(d) 3√3The question was posed to me in a job interview.Query is from Zeros and Coefficients of Polynomial in section Polynomials of Mathematics – Class 10

Answer»

The correct answer is (b) √3

To EXPLAIN: α and β are the zeros of x^2 – (5 + 7k)x + 35K

So, α + β = (5 + 7k) and αβ = 35k

Also, α^2 + β^2 = 172

(α + β)^2 – 2αβ = 172

Substituting VALUES we get,

(5 + 7k)^2 – 2(35k) = 172

25 + 49k^2 + 70K – 70k = 172

49k^2 – 147 = 0

Solving we get, k = √3



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