## 1. A polynomial of degree zero is called:

### Answer:

### Explanation:

A polynomial of degree zero has no variable term and is called a constant polynomial.

## 2. The degree of the polynomial 5x^3 – 4x^2 + 7x – 8 is:

### Answer:

### Explanation:

The highest power of the variable x is 3, so the degree is 3.

## 3. If p(x) = ax^2 + bx + c, where a ≠ 0, then p(x) is a:

### Answer:

### Explanation:

A polynomial of degree 2 is called a quadratic polynomial.

## 4. The number of zeros of a quadratic polynomial is:

### Answer:

### Explanation:

A quadratic polynomial can have at most 2 zeros.

## 5. The value of polynomial p(x) = x^2 – 4 at x = 2 is:

### Answer:

### Explanation:

p(2) = 2^2 – 4 = 4 – 4 = 0.

## 6. Which of the following is NOT a polynomial?

### Answer:

### Explanation:

A polynomial doesn't have negative exponents, so x^-2 + 3x + 7 is not a polynomial.

## 7. The zeros of the polynomial x^2 – x are:

### Answer:

### Explanation:

The polynomial can be factored as x(x-1). So, the zeros are 0 and 1.

## 8. If one zero of the polynomial p(x) = 3x^2 – kx + 6 is 2, the value of k is:

### Answer:

### Explanation:

For x=2, p(2) = 0 => 12 – 2k + 6 = 0 => k = 12.

## 9. The polynomial p(x) = x^3 – 6x^2 + 11x – 6 has how many zeros?

### Answer:

### Explanation:

A cubic polynomial has at most 3 zeros.

## 10. Which of the following polynomials has no real zeros?

### Answer:

### Explanation:

The discriminant is negative for the polynomial x^2 + 1, so it has no real zeros.

## 11. The sum of the zeros of the polynomial x^2 – 5x + 6 is:

### Answer:

### Explanation:

The sum of zeros is given by -b/a = 5/1 = 5.

## 12. The polynomial formed by the zeros 3 and 2 is:

### Answer:

### Explanation:

(x-3)(x-2) = x^2 – 5x + 6.

## 13. If one zero of the polynomial x^2 + px + 12 is -4, the value of p is:

### Answer:

### Explanation:

Sum of zeros is -b/a = -p, other zero = p+4. Since one zero is -4, p+4=0 => p=-4. However, p+4 = -p => 2p = -4 => p = -2 (Incorrect options provided).

## 14. Which of the following polynomials has the same zeros as x^2 – 2x + 1?

### Answer:

### Explanation:

x^2 – 2x + 1 can be written as (x-1)(x-1). Similarly, x^2 – 4x + 4 can be written as (x-2)(x-2).

## 15. The product of the zeros of the polynomial x^2 + 7x + 10 is:

### Answer:

### Explanation:

The product of zeros is given by c/a = 10/1 = 10.

## 16. Which of the following is a polynomial in one variable?

### Answer:

### Explanation:

A polynomial in one variable has terms in only one variable.

## 17. The degree of the zero polynomial is:

### Answer:

### Explanation:

The degree of the zero polynomial is not defined.

## 18. If α and β are the zeros of the polynomial x^2 – x – 6, then α + β + αβ is:

### Answer:

### Explanation:

α + β = 1 and αβ = -6. Therefore, α + β + αβ = 1 – 6 = -5 (Incorrect options provided).

## 19. The number of zeros of the polynomial 2x^3 – 3x^2 + 2x – 1 is:

### Answer:

### Explanation:

A cubic polynomial has at most 3 zeros.

## 20. The polynomial represented by the graph that touches the x-axis but does not cross it has how many zeros?

### Answer:

### Explanation:

If a polynomial's graph touches the x-axis but doesn't cross it, it has a repeated zero at that point.