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Example 9 - Find all zeroes of 2x4 - 3x3 - 3x2 + 6x - 2 - Examples

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Example 9 (Introduction) Find all the zeroes of 2x4 – 3x3 – 3x2 + 6x – 2, if you know that two of its zeroes are √2 and − √2 . 2 is a factor of 6 3 is a factor of 6 So, 2 × 3 is also a factor of 6 We will use the same in our question Example 9 Find all the zeroes of 2x4 – 3x3 – 3x2 + 6x – 2, if you know that two of its zeroes are √2 and − √2 . Let p(x) = 2𝑥4−3𝑥3−3𝑥2+6𝑥 −2 Since x = √2 is a zero , x – √2 is a factor Since x = – √2 is a zero , x + √2 is a factor Hence , (x + √2) (x - √2) is a factor i.e. (x2 – (√2)^2) is also a factor i.e. (x2 – 2) is also a factor Now by dividing the given polynomial by (x2 – 2) We can find out other factors Now, we factorize 2x2 – 3x + 1 2x2 – 3x + 1 We use splitting the middle term method = 2x2 – 2x – x + 1 = 2x(x – 1) – 1 (x – 1) = (2x – 1)(x – 1) ∴ x = 1/2 & x = 1 are zero of p(x) Therefore, the zeroes of p(x) are √2, –√2, 1/2, and 1.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.