Ex 2.4 Class 10 Maths Question 4
If two zeroes of the polynomial x^4 - 6x^3 - 26x^2 + 138x - 35 are 2 + or - √3, find other zeroes
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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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