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.

Answer 1

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.