If two zeros of the polynomial x*- 6×3 – 26x + 138x – 35 are 2 + 13, find other zeroes

2 thoughts on “If two zeros of the polynomial x*- 6×3 – 26x + 138x – 35 are 2 + 13, find other zeroes”

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   9th>Maths>Polynomials>Remainder Theorem>If two zeroes of

   The two zeroes of the polynomial is 2+3,2−3

   Therefore, (x−2+3)(x−2−3)=x2+4−4x−3

   = x2−4x+1 is a factor of the given polynomial.

   Using division algorithm, we get

   x4−6×3−26×2+138x−35=(x2−4x+1)(x2−2x−35)

   So, (x2−2x−35) is also a factor of the given polynomial.

   x2−2x−35=x

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2. The two zeroes of the polynomial is 2+

   3

   ,2−

   3

   Therefore, (x−2+

   3

   )(x−2−

   3

   )=x

   2

   +4−4x−3

   = x

   2

   −4x+1 is a factor of the given polynomial.

   Using division algorithm, we get

   x

   4

   −6x

   3

   −26x

   2

   +138x−35=(x

   2

   −4x+1)(x

   2

   −2x−35)

   So, (x

   2

   −2x−35) is also a factor of the given polynomial.

   x

   2

   −2x−35=x

   2

   −7x+5x−35

   =x(x−7)+5(x−7)

   =(x−7)(x+5)

   Hence, 7 and −5are the other zeros of this polynomial

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