Linear and Quadratic Equations

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What is the value of x+y ?

Progressions and Equations

    Let x3- x2 + bx + c = 0 has 3 real roots which are in A.P. which of the following could be true
    1. b=2,c=2
    2. b=1,c=1
    3. b= -1,c = 1
    4. b= -1,c= -1

 

  • Correct Answer
    Choice B. 9

Detailed Solution

Given the roots are in A.P. so let a-d, a, a+d be the roots
From equation, sum of roots = 1
Sum of two roots taken at a time = +b
Product of two roots = -c
∴ (a-d)+ (a)+ (a+d) = 1
=) 3a = 1
=) a =
Also, (a-d)a+ a(a+d)+ (a-d)(a+d) = b
=) a2 – ad + a2 + ad + a2 – d2 = b
=) 3a2 – d2 = b
=) 3x – d2 = b
=) d2 = b -
Now, since d is a real number,

Also,
(a-d)(a)(a+d) = -c
=) a(a2 – d2) = -c
=)
=)
=)
=)
Again,

∴ Only option (c) b= -1 , c =1 could be true .


Correct Answer: 9



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