Question

(1) Prove that the expression x^2 - (a+b+c)x+a^2+b^2+c^2+2bc -ca-ab can never be negative if x,a,b,c, are real.
(2) prove that if the roots of ax^2 +bx+c = 0 are real so also are the roots of acx^2+(2ac-b^2)x +ac=0
(3)for that values of m is it possible to express 2x^2+3y^2+7xy+4x+my+z as the product of two factors linear in x and y .

Answer 1

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