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CBSE Class 10 Answered

Page 72 If one root of the two quadratic equations x2 + ax + b = 0 and x2  + bx + a = 0 is common , then a +  b = 1 a +  b = -1 ab = 1 ab = -1
Asked by miniprasad | 21 Sep, 2018, 07:38: PM
answered-by-expert Expert Answer
If quadratic euqations are a1 x2 + b1 x + c1 = 0 and a2 x2 + b2 x + c2 = 0 and having one common root (α) then 
α = begin mathsize 16px style fraction numerator straight c subscript 1 straight a subscript 2 minus straight c subscript 2 straight a subscript 1 over denominator straight a subscript 1 straight b subscript 2 minus straight a subscript 2 straight b subscript 1 end fraction end style
Comparing with given quadratic equations we get 
 
a1 = 1, b1 = a, c1 = b, a1 = 1, b1 = b, c1 = a
Using the above formula we get α = 1
Also,
α + β = -a hence, β = -a - 1........(i)
α β = b hence, β = b..........(ii)
α + γ = -b hence, γ = -b - 1
α γ = a hence, γ = a
Using (i) and (ii)
b = -a - 1
a + b = -1
 

Answered by Sneha shidid | 26 Sep, 2018, 10:01: AM

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