3. Let f = ax² + bx + c, for a, b, c real numbers and a ± 0. Prove that f is a prime in R[x] if and only if b² – 4ac < 0. Prove that if 6ª - 4ac = D 2 0 then 1- a(x - )( - -). -b + VDy - VD

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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3. Let f = ax? + bx + c, for a, b, c real numbers and a + 0. Prove that
f is a prime in R[x] if and only if b?
4ас3D D 2 0 then
4ac < 0. Prove that if b2 -
-b + VD
-b
* -
2a
2a
Transcribed Image Text:3. Let f = ax? + bx + c, for a, b, c real numbers and a + 0. Prove that f is a prime in R[x] if and only if b? 4ас3D D 2 0 then 4ac < 0. Prove that if b2 - -b + VD -b * - 2a 2a
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