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.

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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