Question

if the zeroes of the polynomial x square +px +q are double in value if the zeroes of 2x square - 5x +3, find p and q

Answer 1

x^2+px+q. ......1
in first equation,
zeroes are
alpha and beta

p=alpha +beta. ..........3
q=alpha x beta. ...........4

these values are double of the second equation
2x^2+5x+3. ........2
here, zeroes of the polynomial are
5=(alpha +beta)/2. .........5
3=(alpha x beta)2. ........6

10=alpha +beta. ..... (from equation 5)
6=alpha x beta. ..... (from equation 6)

by comparing equations 3 and 5. and. 4 and 6
we get,
p=10
q=6