Question

Prove that roots of a²x² + (b²+a²-c²)x + b² = 0 are not real if a, b and c are sides of a triangle.

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Answer 1

Answer:

Roots of the quadratic equation ax2+bx+c=0 are non real.

⇒b2−4ac<0 -----(1)

Now, for the expression a

2x2+abx+ac,

Δ=a2b2−4a3c=a2 (b2−4ac)<0 from (1)

Since, discriminant value is less than zero, coefficient of x

2 and expression always have same sign.

∴a2x2+abx+ac>0

Hence, option A.