Polynomials — Important Questions

2x³ + 3x - 1, 5x² - 2x + 7, x⁴ - 2x³ + x

Polynomials contain only non-negative integer powers of variables. Options with 1/x, √x are not polynomials as they contain negative or fractional powers.

It is a quadratic polynomial, Its degree is 2, It has zeroes 3 and 4

x² - 7x + 12 = (x - 3)(x - 4), so it's quadratic (degree 2) with zeroes 3 and 4. The constant term is 12, not 7.

3

For quadratic ax² + bx + c, sum of zeroes = -b/a. Here a = 1, b = -3, so α + β = -(-3)/1 = 3.

-2

The coefficient of x² is the number multiplying x². In 5x³ - 2x² + 4x - 1, the term with x² is -2x², so the coefficient is -2.