D If two zeroes of the polynomial ar-6r-26138x-35 are 2t 3, find other

1.	D If two zeroes of the polynomial ar-6r-26138x-35 are 2t 3, find other zeroes.
Answer» Since 2+ √3 is a zero,x-(2+√3) is a factor of the polynomial. Since 2-√3 is a zero,x-(2-√3) is a factor of the polynomial. This means that (x-2-√3)(x-2+√3) are factors (x-2-√3)(x-2+√3) [ using identity ]= (x-2)² - (√3)² = x² -4x +4 - 3= x²- 4x+1 x²- 4x+1 is a factor of x⁴-6x³-26x²+138x-35 WE have to perform division algorithm ,divide x⁴-6x³-26x²+138x-35 with x²- 4x+1 we get the answer as :- x²- 2x - 35 Now split the middle terms !! x²- 7x + 5x - 35 x [ x - 7 ] + 5 [ x - 7 ] [ x+ 5 ] [ x - 7 ] The other zeroes are :- -5 and 7 Like my answer if you find it useful!

D If two zeroes of the polynomial ar-6r-26138x-35 are 2t 3, find other zeroes.

Answer»

Since 2+ √3 is a zero,x-(2+√3) is a factor of the polynomial.

Since 2-√3 is a zero,x-(2-√3) is a factor of the polynomial.

This means that (x-2-√3)(x-2+√3) are factors

(x-2-√3)(x-2+√3) [ using identity ]= (x-2)² - (√3)² = x² -4x +4 - 3= x²- 4x+1

x²- 4x+1 is a factor of x⁴-6x³-26x²+138x-35

WE have to perform division algorithm ,divide x⁴-6x³-26x²+138x-35 with x²- 4x+1

we get the answer as :-

x²- 2x - 35

Now split the middle terms !!

x²- 7x + 5x - 35

x [ x - 7 ] + 5 [ x - 7 ]

[ x+ 5 ] [ x - 7 ]

The other zeroes are :-

-5 and 7

Like my answer if you find it useful!