Quadratic Equations, SPM Practice (Paper 2)


Question 4:
It is given α and β are the roots of the quadratic equation x (x – 3) = 2k – 4, where k is a constant.
(a) Find the range of values of k if αβ.(b) Given α2 and β2 are the roots of another quadratic equation     2x2+tx4=0, where t is a constant, find the value of t and of k.

Solution:
(a)x(x3)=2k4x23x+42k=0a=1, b=3, c=42k                   b24ac>0(3)24(1)(42k)>0               916+8k>0                            8k>7                              k>78

(b)From the equation x23x+42k=0,α+β=ba         =31         =3.............(1)αβ=ca    =42k1    =42k.............(2)From the equation 2x2+tx4=0,α2+β2=t2α+β=t.............(3)α2×β2=42αβ=8.............(4)Substitute (1)=(3),3=tt=3Substitute (2)=(4),42k=84+8=2kk=6