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Question
If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial 2x2 – 5x – 3, then find the values of p and q.
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Solution
f(x) = 2x2 – 5x – 3
Let the zeroes of the polynomial be α and β, then
Sum of zeroes = α + β = `5/2`
Product of zeroes = αβ = `-3/2`
According to the question, zeroes of x2 + px + q are 2α and 2β
Sum of zeroes = `- ("Coefficient of" x)/("Coefficient of" x^2) = (-p)/1`
–p = 2α + 2β = 2(α + β)
–p = `2 xx 5/2` = 5 or p = –5
Product of zeroes = `"Constant term"/("Coefficient of" x^2) = q/1`
q = 2α × 2β = 4αβ
q = `4 (- 3/2)` = –6
p = –5 and q = –6.
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