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  • Suppose a,b belong R . If the Equation x^2-(2a+b)x+(2a^2+b^2-b+1/2) =0 has two real roots , then a,b=?

Suppose a,b belong R . If the Equation x^2-(2a+b)x+(2a^2+b^2-b+1/2) =0 has two real roots , then a,b=?

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Solution: As  Equation has real roots,

\ (2a+b)^2-4(2a^2+b^2-b+1/2)geq 0\ \Rightarrow 4a^2+3b^2-4ab-4b+2leq 0\ \Rightarrow (2a-b)^2+2(b-1)^2leq 0Rightarrow b=1,a=2

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Deependra Verma

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