Question

If α and β are the zeros of x^2+35x-75, then _______

(a) α+β<αβ

(b) α+β>αβ

(c) α+β=αβ

(d) α+β≠αβ

This question was addressed to me in an interview.

The above asked question is from Zeros and Coefficients of Polynomial topic in section Polynomials of Mathematics – Class 10

Answer 1

The correct answer is (b) α+β>αβ

For explanation: The given polynomial is x^2+35x-75.

The sum of zeros, α + β = \(\frac {-coefficient \, of \, x}{coefficient \, of \, x^2} = \frac {-35}{1}\) = -35

The product of zeros, αβ = \(\frac {constant \, term}{coefficient \, of \, x^2}\) = -75

Clearly, sum of zeros is greater than product of zeros.