1)if alpha and beta are the zeros of the polynomial x2 -6x +k,what is the value of k when 3 alpha + 2 beta =20

2)if alpha and beta are the zeros of the polynomial 2x2 +7x -3, then the value of 1/alpha +1/beta

3)the quadratic polynomial p(x) with -81 and 3 as product and one of the zeros respectively.what is the polynomial

4)if x+1 is a factor of 2x3 +ax2+2bx +1 find the values of a and b where 2a-3b=4

5)if one solution of the equation 3x2-8x+3k+1 is seven times the other find the soultions and the valure of k

6)if one zero of the polynomial(a2+4)x2 +13x +4a is the reciprocal of the other,find the value of 'a'

(7)if alpha and beta are the zeroes of the quadratic polynomial x2-(k+6)x + 2(2k-1),find k such that alpha + beta =1/2alphabeta

(8)find the values of a and b such that x4+x3+8x2+ax+b is divisible by x2+1

(9) when the polynomial 4x4-5x3-39x2-40x-2 wadivided by the polynomial g(x) the quotient and the remainder were x2-3x-5 and -3x+8 respectively.Find g(x) .

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  • -3

  It is not possible to answer these ques. in one time. Therfore i can give u hints or way to solve..

1)Here, alpha + beta = -b/a  =  6  &  alpha *beta = c/a = k

given,3alpha+2beta = 20  ..  now square on both side & put the values of alha + beta and alpha * beta

then, u get your required result..

2) alpha +beta = -b/a = -7/2 & alpha*beta = c/a = -3/2

now, 1/alpha + /beta = alpha + beta/ alpha *beta

  = -7/2  = 7/3


3) let alpha =3 & alpha * beta = -81

therefore, beta = -81/3 = -27

hence, required polynomial = k[x2- [alpha +beta] + [alpha+beta]       =k{x2-[-27-3]x +[-81]}

  = k [ x2+30x - 81]

  • -7

if x+1 is a factor then x=-1 is a zero

therefore, p[ -1 ] = 2[ -1]3+a[ -1]2+2b[ -1] +1

  0 = -2+a -2b+1

  1 = a-2b  .................A

given,2a -3b = 4  ..................B

Now, solve a&b by elimination method,which is required answer.

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Rest of the questions are similar, try to do them.If u have any problem see R.D. Sharma textbook.


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