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Example 3 - Find zeroes of polynomial x2 - 3 and verify - Examples

  1. Chapter 2 Class 10 Polynomials
  2. Serial order wise
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Example 3 Find the zeroes of the polynomial x2 – 3 and verify the relationship between the zeroes and the coefficients. Let p(x) = x2 – 3 Zero of the polynomial is the value of x where p(x) = 0 Putting p(x) = 0 x2 – 3 = 0 (x)2 – (√3)2 = 0 Using a2 – b2 = (a – b)(a + b) (x − √3)(x + √3) = 0 So x = √3 , –√3 Therefore, α = √3 & β = -√3 are zeroes of the polynomial We can write p(x) = x2 – 3 = x2 + 0 – 3 = 1x2 + 0(x) – 3 It is of the form ax2 + bx + c So, a = 1, We have to verify Sum of zeroes = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α + β = - 𝑏/𝑎

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