Question

If two zeros of the polynomial x*- 6x3 - 26x + 138x - 35 are 2 + 13, find other zeroes

Answer 1

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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Answer 2

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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

x4−6x3−26x2+138x−35=(x2−4x+1)(x2−2x−35)

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

x2−2x−35=x