Question

d) The extreme terms in the proportion 12:18:2:3 are 18 and 2.
State whether the following statements are True (T) or False (F).
a) The word 'proportion' is denoted by the symbol'.
b) 7: 14 and 15:30 are in proportion.
c) If a:b = c:d then a, b, d and care in proportions
e) If a, b, c, d are in proportion then ad-bc = 0.​

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.