Which of the following is not a zero of the polynomial x3 – 6x2 + 11

1.	Which of the following is not a zero of the polynomial x3 – 6x2 + 11x – 6? A) 1 B) 2 C) 3 D) 0
Answer» Correct option is (D) 0 Let \(p(x)=x^3 – 6x^2 + 11x – 6\) \(\because\) p(0) = -6 \(\neq\) 0 \(\therefore\) 0 is not a zero of given polynomial p(x). Alternative :- \(p(x)=x^3 – 6x^2 + 11x – 6\) \(=x^3-x^2-5x^2+5x+6x-6\) \(=x^2(x-1)-5x(x-1)+6(x-1)\) \(=(x-1)(x^2-5x+6)\) \(=(x-1)(x-2)(x-3)\) \(\therefore\) 1, 2 & 3 are zeros of given polynomial p(x). Correct option is D) 0

Which of the following is not a zero of the polynomial x3 – 6x2 + 11x – 6? A) 1 B) 2 C) 3 D) 0

Answer»

Correct option is (D) 0

Let \(p(x)=x^3 – 6x^2 + 11x – 6\)

\(\because\) p(0) = -6 \(\neq\) 0

\(\therefore\) 0 is not a zero of given polynomial p(x).

Alternative :-

\(p(x)=x^3 – 6x^2 + 11x – 6\)

\(=x^3-x^2-5x^2+5x+6x-6\)

\(=x^2(x-1)-5x(x-1)+6(x-1)\)

\(=(x-1)(x^2-5x+6)\)

\(=(x-1)(x-2)(x-3)\)

\(\therefore\) 1, 2 & 3 are zeros of given polynomial p(x).

Correct option is D) 0