Polynomials: Practice Set 1

The zeroes of the polynomial \(x^2 - 2x - 8\) are

If a polynomial \(p(x)\) is given by \(p(x) = x^2 - 5x + 6\), then the value of \(p(1) + p(4)\) is:

If \(\alpha\) and \(\beta\) are the zeroes of \(x^2 - 5x + 6\), then \(\alpha^2 + \beta^2\) equals

The quadratic polynomial, the sum of whose zeroes is \(-5\) and their product is 6, is

Which of the following is a quadratic polynomial having zeroes \(-\dfrac{2}{3}\) and \(\dfrac{2}{3}\)?

The zeroes of the polynomial \(x^2 - 9\) are

A quadratic polynomial whose zeroes are 2 and 3 is

If the zeroes of \(ax^2 + bx + c\) are reciprocals of each other, then

Assertion (A): The polynomial \(4x - 3\) has exactly one zero.
Reason (R): A linear polynomial \(ax + b\), \(a \neq 0\), has exactly one zero, namely \(-\dfrac{b}{a}\).

Assertion (A): 0 is a zero of the polynomial \(x^3 - 2x^2 + x\).
Reason (R): The constant term of \(x^3 - 2x^2 + x\) is 0.