Question

If the graph of the quadratic polynomial is completely above or below the x-axis, then the nature of roots of the polynomial is _____

(a) Real and Distinct

(b) Distinct

(c) Real

(d) Complex

I had been asked this question in an online quiz.

Enquiry is from Geometrical Meaning of Zeros of Polynomial in portion Polynomials of Mathematics – Class 10

Answer 1

Right answer is (d) Complex

For explanation I would say: Since, the graph is completely above or below the x-axis, hence, it has no real roots. If a polynomial has real roots only then it cuts the x-axis. If it lies above or below, the roots are complex in nature.