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sunil kumar

· started a discussion

· 1 Months ago

nice question (Question: 111086.0 )

Keep it up Rankers. avoid repetion

Question:
If a and b are non-zero roots of x2+ax+b = 0, then the least value of x2+ax+b is :
Options:
A) \(\cfrac{2}{3}\)
B) \(-\cfrac{9}{4}\)
C) \(\cfrac{4}{3}\)
D) 1
Solution:
Ans: (b)

Given that a and b are the roots of the equation x2 + ax +b = 0  

Then sum of roots a + b = -a

b = - 2a

and product of roots ab = b

ab - b = 0

b (a-1) = 0

If b = 0 then a =0

If b \(\neq\) 0 then a = 1 and b = -2

\(\therefore\) x2+ x - 2

\(x^2+x+\cfrac{1}{4}-\cfrac{1}{4}-2\Rightarrow \left ( x+\cfrac {1}{2} \right )^2-\cfrac{9}{4}\)

\(\therefore\) least value of x2+x-2 is \(\cfrac{-9}{4}\)

Knowledge Expert

· commented

· 1 Months ago

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