The expression x^2 + 2bx + c has the positive value if - Vidyadip

MCQ

The expression ${x^2} + 2bx + c$ has the positive value if

A
${b^2} - 4c > 0$
B
${b^2} - 4c < 0$
C
${c^2} < b$
✓
${b^2} < c$

✓

Answer

Correct option: D.

${b^2} < c$

d
(d) ${x^2} + 2bx + c = {(x + b)^2} + c - {b^2}$

$\because$ ${(x + b)^2}$ is a perfect square,

therefore the given expression is positive if $c - {b^2} > 0$or ${b^2} < c$.

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