Dilpreet S. 2 Answers By Expert Tutors
Andrew M. answered • 09/22/18 Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
p(x) = x3 - 6x2 + 11x - 6 If there is a zero at x=2 then (x-2) is a factor If there is a zero at x=3 then (x-3) is a factor (x-2)(x-3)(y) = x3 - 6x2 + 11x - 6 y = (x3 - 6x2 + 11x - 6)/[(x-2)(x-3)] y = (x3 - 6x2 + 11x - 6)/(x2 - 5x + 6) ------------------------------- x2-5x+6 | x3 - 6x2 + 11x - 6 -------------------------- The final factor of the polynomial is (x-1) p(x) = (x-1)(x-2)(x-3) = x3 - 6x2 + 11x - 6
Then x^2 - 5x + 6 is a factor Dividing p(x) by this quadratic results in a quotient of x-1 So X=1 is the third zero.
Let f(x) = 2x3 - x2 - 5x - 2 Here a = 2, b = -1, c = -5 and d = -2 The zeroes will be α = -1, β = 2 and γ = ? Sum of zeroes, α + β + γ = -b/a -1 + 2 + γ = -(-1)/2 γ + 1 = 1/2 γ = -1/2 So, the third zero is -1/2 Given polynomial Let p, q and r are three zeroes of polynomial We know,p*q*r = - d/a = -(-2)/2 = 1 p*q*r = 1......(2) Put value of p*q from eq(1) in eq(2) Therefore, third zero is - 1/2 |