## Chapter 2: Polynomials

**Q1. The zeroes of x ^{2}–2x –8 are:**

(a) (2, -4)

(b) (4, -2)

(c) (-2, -2)

(d) (-4, -4)

Answer: **(b) (4, -2)**

**2. What is the quadratic polynomial whose sum and the product of zeroes is √2, ****⅓**** respectively?**

(a) 3x^{2}-3√2x+1

(b) 3x^{2}+3√2x+1

(c) 3x^{2}+3√2x-1

(d) None of the above

Answer: **(a) 3x ^{2}-3√2x+1**

**3. If the zeroes of the quadratic polynomial ax ^{2}+bx+c, c≠0 are equal, then**

(a) c and b have opposite signs

(b) c and a have opposite signs

(c) c and b have same signs

(d) c and a have same signs

Answer: **(d) c and a have same signs**

**4. The degree of the polynomial, x ^{4} – x^{2} +2 is**

(a) 2

(b) 4

(c) 1

(d) 0

Answer: **(b) 4**

**5. If one of the zeroes of cubic polynomial is x ^{3}+ax^{2}+bx+c is -1, then product of other two zeroes is:**

(a) b-a-1

(b) b-a+1

(c) a-b+1

(d) a-b-1

Answer: **(b) b-a+1**

**video tutorial of the above questions**

**6. If p(x) is a polynomial of degree one and p(a) = 0, then a is said to be:**

(a) Zero of p(x)

(b) Value of p(x)

(c) Constant of p(x)

(d) None of the above

Answer: **(a) Zero of p(x)**

**7. A polynomial of degree n has:**

(a) Only one zero

(b) At least n zeroes

(c) More than n zeroes

(d) At most n zeroes

Answer: **(d) At most n zeroes**

**8. The number of polynomials having zeroes as -2 and 5 is:**

(a) 1

(b) 2

(c) 3

(d) More than 3

Answer: **(d) More than 3**

**9. Zeroes of p(x) = x ^{2}-27 are:**

(a) ±9√3

(b) ±3√3

(c) ±7√3

(d) None of the above

Answer: **(b) ±3√3**

**10. If one zero of the quadratic polynomial x ^{2} + 3x + k is 2, then the value of k is**

(a) 10

(b) –10

(c) 5

(d) –5

Answer: **(b) -10**

**11. A quadratic polynomial, whose zeroes are –3 and 4, is**

(a) x² – x + 12

(b) x² + x + 12

(c) (x²/2) – (x/2) – 6

(d) 2x² + 2x – 24

Answer: **(c) (x²/2) – (x/2) – 6**

**12. The zeroes of the quadratic polynomial x ^{2}**

**+ 99x + 127 are**

(a) both positive

(b) both negative

(c) one positive and one negative

(d) both equal

Answer: **(b) both negative**

**13. The zeroes of the quadratic polynomial x ^{2}**

**+ 7x + 10 are**

(a) -4, -3

(b) 2, 5

(c) -2, -5

(d) -2, 5

Answer:** (c) -2, -5**

**14. If the discriminant of a quadratic polynomial, D > 0, then the polynomial has**

(a) two real and equal roots

(b) two real and unequal roots

(c) imaginary roots

(d) no roots

Answer: **(b) two real and unequal roots**

**15. By division algorithm of polynomials, p(x) =**

(a) g(x) × q(x) + r(x)

(b) g(x) × q(x) – r(x)

(c) g(x) × q(x) × r(x)

(d) g(x) + q(x) + r(x)

Answer: **(a) g(x) × q(x) + r(x)**

By division algorithm of polynomials, p(x) = g(x) × q(x) + r(x).

**16. If the graph of a polynomial intersects the x-axis at three points, then it contains ____ zeroes.**

(a) Three

(b) Two

(c) Four

(d) More than three

Answer: **(a) Three**

**video tutorial: (from Q6 to Q16)**