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If the zeros of the polynomial …

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If the zeros of the polynomial f(x)= x^3-3x^2+x+1 are (a-b), a and (a+b), find a & b.
  • 2 answers

King?Adithya H. M.. 4 years, 8 months ago

Prakash 13:33 Hey, glad to know that you're learning from BYJU'S. For more help you may chat here. Student 13:33 If the zeros of the polynomial f(x)= x^3-3x^2+x+1 are (a-b), a and (a+b), find a & b. Read New message Prakash 13:34 Kindly allow me a minute or two to check for relevant answers to your question. Please be online. Prakash 13:35 ANSWER a−b,a,a+b are zeroes of x 3 −3x 2 +x+1 ⇒a−b+a+a+b= sum of zeroes = 3 ⇒3a=3 ⇒a=1 (a−b)(a)(a+b)= product of zeroes =−1 ⇒(1−b)(1+b)=−1 ⇒1−b 2 =−1 ⇒b 2 =2 ⇒b=± 2 ​

Gaurav Seth 4 years, 8 months ago

sum of the zeroes = (a-b) + (a+b) + a = 3a i.e. 3a = - b/a

                                                                       or  3a=3

                                                                       or  a=1

product of the zeroes = (a-b)*(a+b)*a= a3-ab2  i.e. 1 - b2 = c/a      (by putting the value a=1)

                                                                                     or b2 =2

                                                                                     or b = +-root2

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