Find all the zeroes, if two of its zeroes are 2 and -2
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Class 10th, rd sharma polynomials
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Find all the zeroes of the polynomial x4 + x3 – 34×2 – 4x + 120, if the two of its zeros are 2 and -2.
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Solution:
Let,
f(x) = x4 + x3 – 34x2 – 4x + 120
Since two of the zeroes of the polynomial are −2 and 2 so, (x + 2) and (x – 2) are factors of f(x).
⇒ x2 – 4 is a factor of f(x). Hence, performing division algorithm, we get
⇒ f(x)= (x2 + x – 30)( x2 – 4)
So, by putting x2 + x – 30 = 0, we can get the other 2 zeros.
⇒ (x + 6)(x – 5) = 0
∴ x = -6 or 5
Hence, all the zeros of the polynomial are 5, -2, 2 and -6.