Relationship Between Zeroes and Coefficients of a Cubic Polynomial
Question 1 ii...
Question
Question 1 (ii)
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.
iii) −2√3,−9
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Solution
iii) Given that, sum of zeroes (S)=−2√3
and product of zeroes (P)=−9 ∴ Required quadratic expression f(x)=x2–Sx+P=x2+2√3x–9 =x2+3√3x−√3x−9 =x(x+3√3)–√3(x+3√3) =(x+3√3)(x−√3)
Hence, the zeroes of f(x) are - 3√3and√3