Chapter 1: Polynomials Chapter-1: Polynomials Level – I (QUESTIONS EXACTLY COPIED FROM NCERT) 1. Which of the following expressions is/are polynomials in one variable? 2 II. y + 2 2 I. 4 x 2 − 3x + 7 III. 3 t + t 2 IV. y + y (a) Only I (b) I & II (c) III & IV (d) All 2. The coefficients of x in 2 x − 1 is 2 (a) 2 (b) 0 (c) –1 (d) Not defined 3. The degree of polynomial ‘3’ is (a) 1 (b) 0 (c) not defined (d) constant 4. Classify the following as cubic polynomials: I. x2 + x II. x − x3 III. 3t IV. 7x3 (a) Only I (b) Only III (c) II & IV (d) I, III & IV 5. The zeroes of the polynomial x + 2 is (a) 2 (b) –2 (c) 2 (d) 3 6. Find the value of polynomial 5x − 4 x 2 + 3 at x = −1 (a) 6 (b) –6 (c) 2 (d) –2 7. The value of p ( 2 ) if p ( x ) = ( x − 1)( x + 1) is (a) 0 (b) 1 (c) 2 (d) 3 8. The zero of the polynomial p ( x ) = cx + d ,c 0,c, d are real numbers is (a) − d (b) − c (c) c (d) d c d d c 9. The graphs of y = p ( x ) are given in Fig. below, for some polynomials p ( x ) . Then the number of zeroes of p ( x ) is/are (a) 0 (b) 1 (c) 2 (d) 3 10. The graphs of y = p ( x ) are given in Fig. below, for some polynomials p ( x ) . Then the number of zeroes of p ( x ) is/are (a) 0 (b) 1 (c) 2 (d) 3 Old ICC building, near Firoz Hospital, Sir Syed Nagar, Medical Road, Aligarh: 9997607607, 9997394458 Chapter 1: Polynomials 11. The graphs of y = p ( x ) are given in Fig. below, for some polynomials p ( x ) . Then the number of zeroes of p ( x ) is/are (a) 1 (b) 2 (c) 3 (d) 4 12. The graphs of y = p ( x ) are given in Fig. below, for some polynomials p ( x ) . Then the number of zeroes of p ( x ) is/are (a) 0 (b) 1 (c) 5 (d) 3 13. The quadratic polynomial with the given numbers 0 as sum and 5 as the product of its zeroes is (a) x 2 − 5x + 5 (b) x 2 + 5x + 5 (c) x 2 − 5 x (d) x 2 + 5 14. The graphs of y = p ( x ) are given in Fig. below, for some polynomials p ( x ) . Then the number of zeroes of p ( x ) is/are (a) 0 (b) 1 (c) 2 (d) 3 15. One of the zero of the quadratic polynomial 3x2 – x – 4 is 5 (a) (b) –1 (c) –2 (d) 1 3 16. The quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively is ( (a) k x 2 + 3 x + 2 ) ( (b) k x 2 − 3 x + 2 ) (c) x 2 − x + 6 (d) x 2 + x − 6 17. Other two zeroes of 2x4 – 3x3 – 3x2 + 6x – 2, if you know that two of its zeroes are 2 and – 2. 1 1 1 1 (a) − & −1 (b) − & 1 (c) &1 (d) & −1 2 2 2 2 5 5 18. Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are and – ⋅ 3 3 (a) 1 & −2 (b) −2 & −1 (c) −1& −1 (d) 1 & −1 19. On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x). (a) x2 − x + 1 (b) x2 + x + 1 (c) x2 + x − 1 (d) x2 − x − 1 Old ICC building, near Firoz Hospital, Sir Syed Nagar, Medical Road, Aligarh: 9997607607, 9997394458 Chapter 1: Polynomials 20. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively. (a) x 2 + 2 x 2 − 7 x + 14 (b) x3 + 2 x 2 + 7 x + 14 (c) x3 + 2 x 2 − 7 x − 14 (d) x3 − 2 x 2 − 7 x + 14 21. If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, find a and b? (a) 1, 2 (b) 1, 2 (c) 1, 2 (d) 2 , 3 22. If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 3 , find other zeroes. (a) −5,5 (b) −5,7 (c) −5,−7 (d) 5, 7 23. If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, the value of k and a, respectively are (a) 5, 5 (b) −5, 5 (c) 5,− 5 (d) −5,− 5 LEVEL – II (QUESTIONS BASED ON NCERT) 1. x − 5 is a factor of the cubic polynomial x3 − 3 5x 2 + 13x − 3 5 , , then the zeroes of the Polynomial are. (a) 5 ,3 5 (b) 5 ,−3 5 (c) 3 ,5 (d) 5 2 , 5 2. If one zero of the quadratic polynomial x + 3x + k is 2, then the value of k is: 2 (a) 10 (b) –10 (c) 5 (d) –5 3. If and are the zeroes of the quadratic polynomial x 2 – 2 x – 8, then + + is: (a) 6 (b) –6 (c) –10 (d) 10 4. Given that two of the zeroes of the cubic polynomial ax + bx + cx + d are 0, the third zero is. 3 2 (a) –b/a (b) a/c (c) a/b (d) –d/a 5. The quadratic polynomial formed by the reciprocal of zeroes of the quadratic polynomial x2 – 3x + 2 is: (a) –3x2 + x + 2 (b) 2 x2 – 3x + 1 (c) x2 + 2 x – 3 (d) 2 x2 + 3x –1 6. If the zeroes of the quadratic polynomial ax2 + bx + c,a 0 are equal, then (a) c and a have opposite signs (b) c and b have opposite signs (c) c and a have the same sign (d) c and b have the same sign 7. The two roots of the equations a ( b – c ) x + b ( c – a ) x + c ( a – b ) = 0 are 1 and: 2 c (a − b ) b(c − a ) a (b − c ) c (a − b ) (a) (b) (c) (d) b(c − a ) a (b − c ) b(c − a ) a (b − c ) 8. One of the quadratic polynomial, whose zeroes are –3 and 4, is (a) x 2 − x + 12 (b) x 2 + x + 12 (c) x 2 + x − 12 (d) 2 x 2 + 2 x − 24 Old ICC building, near Firoz Hospital, Sir Syed Nagar, Medical Road, Aligarh: 9997607607, 9997394458 Chapter 1: Polynomials 9. If the zeroes of a quadratic polynomial ax2 + bx + c are both negative, then a, b and c all have the same sign. (a) c and a have opposite signs (b) c and b have opposite signs (c) c and a have the same sign (d) a, c and b have the same sign 10. If the zeroes of the quadratic polynomial x − ( a + 1) x + b are 2 and –3 then. 2 (a) a = – 7, b = –1 (b) a = 5, b = –1 (c) a = 2, b = – 6 (d) a = −2, b = – 6 11. If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative o