1.Find the quadratic equation whose zeroes are 3+sqrt 2 2.If the polynomial 6x^4+8x^3-5x^2+ax+b is exactly divisible by 2x^2-5,find the values of a and b 3.Find all the zeroes of the polynomial x^4+x^3-34x^2-4x+120,if two of its zeroes are 2 and -2 4.Find the quadratic polynomial whose graphs meet the x axis at (-2,0)and (3,0) 5.Can x-3 the remainder of a polynomial p(x) by 3x+2? Justify your answer. 6.Find the zeroes of the polynomial 3x^2-2sqrt3x+1and verify the relationship between zeroes and coefficients. 7.What must be added to 6x^5+5x^4+11x^3-3^x2+x+5 so that it may be exactly divisible by 3x^2-2x+4 8.If alpha and beta are the zeroes of the polynomial x^2+5x+3,evaluate the following. i) alpha ^2+beta ^2 ii)alpha^3+beta^3 iii)alpha^-1+beta^-1 iv)alpha^-2+beta^-2 9.On dividing p(x)=x^3+x^2+x-2 by a polynomial g(x), the quotient and remainder are x^2+2x+1 and 2x-1.Find g(x). 10.If 2and -3 are zeroes of the polynomial x^2+(a+1)x+b.Find. a and b. 11.Find all the zeroes of the polynomial 2x^4-10x^3+5^2+15x-12, if two of its zeroes are sqrt 3/2 -and sqrt 3/2 12.One of the zeroes of the polynomial x^2-4x-k/2 is 5/2.Find the value of k and the other zero 13.If alpha and beta are the zeroes of the polynomial 25p^2-15p+2,Find the quadratic polynomial whose zeroes are 1/2alpha and 1/2beta 14.If one of the zeroes of the polynomial 4x^2-8kx-9 is the negative of the other, find the value of k 15.Write the polynomial, the product and sum of the zeroes are responsibility -9/2 and -3/2 16.Divide 2x-9x+5x+3x-8 by x^2-4x+1 and verify the algorithm 17.If one of the zeroes of the polynomial 4x^2-x+m^2 is the reciprocal of the other, find the value of m. 18.Find the zeroes of the polynomial 3x^2-3/4 and verify the relationship between the zeroes and the coefficients. 19.If alpha and beta are the zeroes of the polynomial x^2-6x+k, find the value of k, if 3alpha +2beta=0 20.Find the values of k and m if the zeroes of the polynomial 3x^2-2kx+2m are 2 and 3
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