F.4 maths

It is given that the quadratic equation ax^2+8x+c=0 has a repeated real root, where a and c are positive integers.
(a) Find all the possible values of a+c.
Discriminant = 64 – 4ac = 0 or ac = 16
Possible combinations of (a,c) are (1,16), (2,8), (4,4), (8,2), (16,1)
The possible values of a+c are 8, 10 and 17
(b) Ken claims that the quadratic equation 2x^2+(a+c)x+10=0 must have real roots. Is he correct? Explain your answer.
Discriminant = (a + c)2 – 4(2)(10)
= (a + c)2 – 80
Since a + c can be 8, and (a + c)2 – 80 = -16, therefore Ken's claim is not correct.