Question

If the zeroes of the polynomial x^2+px+q are double in value to the zeroes of 2x^2-5x-3 find p and q Advertisement

Answer 1

2x2 - 5x - 3 
2x2 - 6x +1x -3 
2x (x - 3) +1 (x - 3) 
(x - 3) (2x+1) 
x = 3, x = -1/2 
so, zeroes of x2 +px+q are 2*3 = 6 and 2 * -1/2 = -1 
let the zeroes be a = 6 and b = -1 
a+b = -coefficient of x/coefficient of x2 
6 + (-1) = -p/1 
5 = -p 
p = -5 
a*b = constant term/coefficient of x2 
6 * (-1) = q/1 
q=-6
so p=-5 and q=-6