Question
The problem I'm having trouble with is #48.
Please write neatly and explain
In Exercises 41 and 42, use the Rational Zeros Test to T possible rational zeros of f(r) 41, f(x) = x4 + 3x3-x2-9x-6 42. f(x) = 9x3-36x2-4x + 16 In Exercises 43-46, use Descartes's Rule of Signs and th Rational Zeros Test to find all real zeros of each polynor function. 43, f(x) = 5x3 + 11x2 + 2x 44. f(x) =x3 + 2x2-5x-6 45. f(x) = x3 + 3r2-1x-12 46. f(x)-= 2x3-9x2 + 12x-5 In Exercises 47-52, find all of the zeros of /(x). real and nonreal, that are not given. 47. /(x) = x3-7x + 6; one zero is 2. , 48. /(x) i =r' + x3-3x2-x| + 2:1 is a zero of multiplicity 2. = 1.4 2x3 + (r2-18.r-27; two zeros are-1 and 3. 50. 32t 2r " 15: one zero is 2 m/i 51, /(x) = 1. t 2x3 t 9s, + 8x + 20:011e zero is-I + 2 1 + 24: 3247 + 64:2 2/ is a zero multiplicity 2 In Exercises 53-58, solve each equation in the complex number system. In Exercises 59 and 60. show that the given equation has no rational roots. 59. In Exercises GI and 62. use the Intermediate Value Theorem to find the value of the real root between 1 and 2 of cach equation to two decimal place
Explanation / Answer
f(x)=x4+x3-3x2-x+2
x=1 is given with a multiplicity of 2
So to find other zeroes, we have to divide by (x-1)2
And on dividing we will get
x2+3x+2
x2+3x+2=0
(x+1)(x+2)=0
x=-1, -2
