Math, asked by Immanuel44, 11 months ago

If two zeros of the polynomial (x4-6x³-26x²+138x-35) are (2+√3) &(2-√3). Find the other zeros....

Answers

Answered by Anonymous
31

SOLUTION:-

Given,

p(x)= 2±√3.

and,

x- (2±√3) are the factors of p(x).

Now,

{x- (2+√3)}{x-(2-√3)}

=) {(x-2) -√3}{(x-2)+√3}

=) (x-2)² - (√3)²

=) x² -4x +1

Therefore,

Dividing p(x) by x² - 4x +1.

For this polynomial;

(x⁴ -6x³ -26x²+138x -35)

Above attachment divide.

Therefore,

p(x)= {x-(2+√3)} {x-(2-√3)} (x² -2x -35)

So,

x² - 2x -35

=) x² +5x -7x -35 =0

=) x(x+5) -7(x+5)=0

=) (x+5) (x-7) =0

=) x+5 =0 or x-7=0

=) x= -5 or x= 7

Hence,

Other two zeroes of p(x) are -5 & 7.

Hope it helps ☺️

Attachments:
Answered by zeenat80100580pa4w5t
2

Answer:

∴7 and −5 are zeros of polynomial

Step-by-step explanation:

Answer

P(n)=x

4

−6x

3

−26x

2

+138−35

as (2+

3

) and (2−

3

) are joas of polynomial of P(a)

So, we divid (R−(2+

3

))(x−(2

3

)) then find quotient

x

2

−2x−

3

x−2x−

3

x+1=x

2

−4x+1

x

2

+4x+1)

x

4

−6x

3

−26x

2

+138x−35

(n

2

−2x−35

x

4

−4x

3

+x

2

___________________________

−2x

3

−27x

2

+138x

−2x

3

+8x

2

−2a

_____________________________

−35x

2

+140x−35

−35x

2

+140x−35

____________________________

0

x

2

−2x−35=x

2

−7x+5x−35=x(x−7)+5(x−7)=0

x=−5,7

∴7 and −5 are zeros of polynomial

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