MULTIPLE CHOICE QUESTIONS

1. Which of the following are not polynomials? ( )

A) i & ii                      B) ii & iii                  C) iii & iv                   D) ii & iv
Ans: D) ii & iv
 

2. The quadratic polynomials among the following ( )

A) i & ii                    B) i & iii                    C) i & iv                      D) ii & iii
Ans: B) i & iii

Ans: B) 4

4. Number of zeroes of polynomial x² - 16 ( )
A) 2                        B) 16                         C) 4                          D) 0
Ans: A) 2
 

5. The graph of y = ax + b where; a, b are real numbers and a ≠ 0 is ( )
A) Parabola           B) Straight line        C) Point            D) None
Ans: B) Straight line
 

6. The graph of y = ax + b where a, b are real numbers and a ≠ 0 intersects x-axis at ( )

Ans: 

7. If the graph of y = ax² + bx + c, a ≠ 0 intersects x-axis at two distinct points then the number of zeros of the polymonimal ax² + bx + c, a ≠ 0 is ( )
A) Zero             B) One           C) Two               D) Three
Ans: C) Two    
 

8. The zeroes of the polynominal p(x) from the following graph y = p(x) are ( )

(i) -1                           (ii) 1                            (iii) 2                              (iv) 3
A) Only i                     B) Only i & ii             C) Only i, ii & iv             D) All of the above
Ans: C) Only i, ii & iv
 

9. The sum of the zeroes of the polynomial ax² + bx + c is ( )

Ans: 

10. The quadratic polynomial whose sum and product of the zeroes are -3 and 2 respectively is ( )
A) -3x² - x + 2            B) x² - 3x + 2          C) x² + 3x + 2               D) x² - 3x - 2
Ans: C) x² + 3x + 2                                                                                                                                                                    
 

11. The value of 'k' if the sum of the zeroes of the polynomial x² - kx + 10 is 12 ( )
A) 10                             B) 12                   C) -12                       D) 1
Ans: B) 12

A) cx² + bx + a           B) bx² + cx + a        C) bx² + ax + c         D) cx² + ax + b
Ans: A) cx² + bx + a
 

13. The sum of the zeroes of a cubic polynomial ax³ + bx² + cx + d is ( )

A) 2x³ + 5x² + 14x + 8                         B) 2x³ - 5x² + 14x + 8
C) 2x³ - 5x² - 14x + 8                           D) 2x³ - 5x² - 14x - 8
Ans: C) 2x³ - 5x² - 14x + 8

15. When a polynomial 2x² + 3x + 1 is divided by x + 2, then the quotient q(x) and remainder r(x) are respectively ( )
A) 2x - 1, 3                B) 2x + 1, 3          C) 2x - 1, -3                 D) 2x + 1, -3
Ans: A) 2x - 1, 3

 

4 marks

1. Find the zeroes of the polynomial x² + 5x + 6 and verify the relationship between the zeroes and the coefficients.
Sol: We have, x² + 5x + 6
= x² + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 2) (x + 3)
The value of x² + 5x + 6 is zero when
x + 2 = 0 or x + 3 = 0
i.e., when x = -2 or x = -3
∴ The zeroes of the polynomial x² + 5x + 6 are -2 and -3
sum of the zeroes = -2 + (-3) = -5 

 

Try this:
* Find the zeroes of the polynomial x² - x - 12 and verify the relationship between the zeroes and the coefficient.