Question

3. 7 If p, 9 and r are real numbers, then roots of the equation (x - p) (x - 2) + (x – 9) (x - ) + (x - p) (x - r) = 0 are equal, if
(1) p = 1, 9 = 1, r = 0
(2) p = q = r
(3) p = 1, 9 = 0, r = 0
(4) 9 = 1, r= 1​

Answer 1

]Both 1 and 2 are correct options.

Given,

4(x−p)(x−q)−r2=0

4x2−4xq−4xp+4pq−r2=0

4x2−(4q+4p)x+4pq−r2=0

x=2⋅4−(−4q−4p)±(−4q−4p)2−4⋅4(4pq−r2)

upon solving the above equation, we get,

x=2q+p±p2−2pq+r2+q2

x=2q+p±(p−q)2+r2

roots are real 

If, p=q,r=0, we have,

4(x−p)(x−p)=0

4(x−p)2=0

(x−p)2=0

x=p

roots are equal

hope it helps you

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Answer 2

Answer:

Agree with her.