Question

if one zero of the polynomial p(x)=x2-6x+k is twice the other then find the value of k

Answer 1

Consider the equation x

2

−6x+q=0, where a = 1, b = -6, c = q

(i) Sum of the roots m+n=

a

−b

=

1

−(−6)

∴m+n=6

(ii) Product of the roots mn=

a

c

=

1

q

∴mn=q

If one root is m then twice the root is 2m.

∴m=m and n=2m

m+n=6∴m+2m=6,3m=6∴m=

3

6

=2

We know that q=mn∴q=m(2m)=2m

2

=2(2)

2

=8∴q=8