Example 2 - Chapter 2 Class 10 Polynomials (Term 1)

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Example 2 Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients. Let p(x) = x2 + 7x + 10 Zero of the polynomial is the value of x where p(x) = 0 Putting p(x) = 0 x2 + 7x + 10 = 0 We find roots using splitting the middle term method x2 + 2x + 5x + 10 = 0 x(x + 2) + 5(x + 2) = 0 (x + 2)(x + 5) = 0 So x = −2, −5 Therefore, α = -2 & β = −5 are the zeroes of polynomial p(x) = x2 + 7x + 10 = 1x2 + 7x + 10 Comparing with 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 Since, L.H.S = R.H.S Hence relationship between zeroes & coefficient is verified