Question

CASE STUDY
In a school thousands of students study in
the class room. Out of them one of the boy
is standing in the ground having
coordinates(4,1) facing towards east. He
moves 4 units in straight line then take
right and moves 3 units and stop.Now he
is at home. The represent of the above
situation on the coordinate axes is shown
below.
4
C
A (4.1)
(a)What is the shortest distance between
his school and house
i)7 units (ii) 3 units (iii) 5 units (iv)4units
(b)Suppose point D divide the line
segment AB in the ratio 1:2,then find the
coordinate of D.
13
16
D3,1 (ii) (3, 1) (ii) (1,1)
(iv) (1, -1)
(c)If we draw perpendicular lines from
points A and B to the X-axis,the region
covered by these perpendicular lines is
i) 3 sq.units (ii)4 sq.units (iii) 5 sq.units
(iv)6 sq.units
(d) Find the area of AABC
i) 5 sq.units (ii) 6 sq.units (iii) 7 sq.units
iv) 8 sq.units
(e) Find the image of points C, w.rt X-axis
i)(-8,-4) (ii) (-8,4) (iii) (8,-4)
(iv) (4,4)​

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.