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Question
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
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Solution
Given: α + β = 4, αβ = 1
α + β = `(-b)/a = 4/1` and αβ = `c/a = 1`
By comparison a = 1, b = -4 and c = 1
Hence, after substituting the values in ax2 + bx + c,
ax2 + bx + c = (1)x2 + (-4)x + 1
= x2 – 4x + 1
Hence, the quadratic polynomial is x2 – 4x + 1.
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