Question
If the sum of the squares of the roots of p2
- (x-2)p - (x+1) = 0 is 5 then what is the value of x.Solution
Let the roots of equation be a and b. Given that, a2 + b2 = 5 We know that, (a+b )2 = a2 + b2 + 2ab Or, (a+b )2 – 2ab = a2 + b2 Sum of roots = -(-(x-2)), product of roots = -(x + 1) (x – 2)2 – 2 × 1 × – (x+1) = 5 Or, x2 + 4 – 4x + 2x + 2 = 5 Or, x2 – 2x + 1 = 0 Or, (p – 1)2 = 0 Or, p = 1
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