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If two zeroes of the polynomial x4 - 6x3 - 26x2 + 138x - 35 are 2 ± √3, find other zeroes
Given polynomial is x4 - 6x3 - 26x2 + 138x - 35 and the zeroes of the polynomial are 2 ± √3
- By using the zeroes of a polynomial, we can find out the factors of the polynomial.
- Now let's divide the polynomial with the factor to get the quotient and remainder.
- Substitute this value in the division algorithm to get the other zeroes by simplifying its factors.
p (x) = x4 - 6x3 - 26x2 + 138x - 35
Zeroes of the polynomial are 2 ± √3
Thus the factors are (x - 2 + √3) and (x - 2 - √3)
(x - 2 + √3)(x - 2 - √3) = x² + 4 - 4x - 3
= x2 - 4x + 1
Thus, x2 - 4x + 1 is a factor of the given polynomial
Now, let's divide x4 - 6x3 - 26x2 + 138x - 35 by x2 - 4x + 1
Clearly, by division algorithm,
x4 - 6x3 - 26x2 + 138x - 35 = (x2 - 4x + 1)(x2 - 2x - 35)
It can be observed that x2 - 2x - 35 is a factor of the given polynomial
Also, x2 - 2x - 35 = x2 - 7x + 5x - 35 = (x - 7) (x + 5)
Therefore, the value of the polynomial is also zero when x - 7 = 0 or x + 5 = 0
Hence, 7 and - 5 are also zeroes of this polynomial.
If two zeroes of the polynomial x⁴ - 6x³ - 26x² + 138x - 35 are 2 ± √3 find other zeroes
NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.4 Question 4
If two zeroes of the polynomial x4 - 6x3 - 26x2 + 138x - 35 are 2 ± √3, the other zeros are 7 and -5.
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