Polynomials - MCQ - Class 10

9. if α and β are the zeros of the polynomial f(x) = x² + x + 1 then what is the value of 1/α + 1/β ?

                a) 1                         b) – 1                     c) 2                         d) -2

10. if one zero of the polynomial f(x) = (k² + 4) x² + 13x + 4k is reciprocal of the other then find the value of k?

                a) 1                         b) -2                       c) 2                         d) -2

11 If the zeros of the polynomial f(x) = x³ – 3px² + qx – r are in AP then

                a) 2p³ = pq – r                                                    b) 2p³ = pq + r   

                c) 2p³ = pq /r                                                      d) p³ = pq /2 – r

12. if if α and β are the zeros of the polynomial f(x) = x² – p(x+1) x – c such that (α + 1) (β+ 1) = 0 then what is the value of c?

                a) 1                         b) 0                        c) -1                       d) 2

13. A quadratic polynomial whose one zero is 6 and sum of the zeroes is 0, is

      (a)   x² – 6x + 2                   (b)   x² – 36                  (c)   x² – 6                     (d)   x² – 3

14. If graph of a polynomial does not intersect the x-axis but intersects y-axis in one point, then no, of zeroes of the polynomial is equal to

      (a)   0                                              (b)   1                                     (c)   0 or 1                            (d)   none of these

15 . Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial

      (a)   intersects y-axis                                                                (b)   intersects x-axis

      (c)   intersects y-axis or intersects x-axis                          (d)   none of these

16. The zeros of the quadratic polynomial x² + 7x + 12 are –

                a) -2, - 5                                b) – 3 , -4                             c) – 5, - 2                              d) -6, -1

17 . Find p and q , if the zeros of the polynomial x³ – 3 x² + x + 1 are p – q , p and p + q

                a) p = ± √2 , q = 1              b) p = √2 , q = 2                  c) p = 2, q = √2                   d) p = 1, q = ±√2

18. if two zeros of the polynomial f(x) = x³ – 4x² – 3x + 12 are sqr root 3 and  - (sqr root 3) then find the third zero?

                a) 2                         b) 4                        c) -5                       d) -1

19 . If p and q are the zeros of the quadratic polynomial 4x² – 1 = 0 , find the value of p² + q²

                a) 3/2                    b) ¼                       c) ½                        d) 1

20. Form a quadratic polynomial of which one zero is 6 - sqr root 5 and the sum of the zeros is 12?

                a) x² – 4x + 30                     b) x² + 4x – 31                     c) x² - 12x – 31                    d) x² - 12x + 31

21. Find the remainder when 2t⁴ – 6t³ + 2t² – t + 2 is divided by t + 2?

                a) 90                                      b) 91                                      c) 92                       d) 93

22. If the sum of the zeros of the polynomial p (x) = 2x³ – 3kx² + 4x – 5 is 6 then the value of k is

                a) 2                         b) 4                        c) -4                       d) 6

23. What is the difference between the values of the polynomial x² - 12x + 31 at x = 1 and x = 2?

                a) 6                         b) 9                        c) -5                       d) 0

24 . If x¹⁰⁰ + 2.x⁹⁹ + k is divisible by x + 1 then the value of k is

                a) 1                         b) 2                        c) 3                         d) -2

NB :- Answer is marked with red colour

Dr Rajesh Kumar Thakur