If a, b, c ∈ Q, then roots of the equation (b+c-2 a) x^2+(c+a-2 b) x+(a+b-2 c)=0 are (a) rational...

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Show that the equation 2(a^2+b^2)x^2+2(a+b)x+1=0 has no real roots, when a≠b.Show that the equation 2(a^2+b^2)x^2+2(a+b)x+1=0 has no real roots, when a≠b.
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If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c.If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c.