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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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 Verifying relationship b/w zeroes and coefficients p(x) = x2 – 3 = x2 + 0 – 3 = 1x2 + 0(x) – 3 It is of the form ax2 + bx + c ∴ a = 1, We have to verify Sum of zeroes = − (𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥)/(𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑥2) i.e. α + β = - 𝑏/𝑎 α + β = √3 − √3 = 0 − 𝑏/𝑎 = − 0/1 = 0 α β = (√3) (–√3) = –(√3)2 = –3 𝑐/𝑎 = (−3)/1 = – 3 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified

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Davneet Singh

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.