Question

True or false : Zero at polynomial x
{x}^{2} + 2 \sqrt{2} x - 6 \sqrt{2} \: 3 \sqrt{2}x2+22​x−62​32​
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Answer 1

Answer:

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 getx 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.