If the zeroes of the polynomial (x^2) +px +q are double in value to the zeroes of the polynomial 2(x^2 )-5x -3, then find the values of p and q.

 If the zeroes of the polynomial (x^2) +px +q are double in value to the zeroes of the
polynomial 2(x^2 )-5x -3, then find the values of p and q.

 

 given expression 2(x^2 )-5x -3

a=2

b = (-5)

c=(-3)

 

using formulae if alpha and beta are the ZEROES of the given polynomial

alpha + beta = (-b)/a = -(-5)/2=5/2

alpha*beta =c/a =(-3)/2

given that the zeroes of

(x^2) +px +q are double in value to the zeroes of the
polynomial 2(x^2 )-5x -3

 

assume the new zeroes are 2alpha and 2beta

sum of new zeroes is 2alpha +2beta = 2(alpha+beta) = 2(5/2)=5

product of the new zeroes are  2alpha *2beta = 4*(alpha*beta) =4*(-3)/2 = (-6)

new polynomial is (x^2) -(sum)x +product

(x^2) -5x -6

compare

(x^2) +px +q

 

to get p =(-5) and q=(-6) 

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