(C) Given the quadratic expression is $(2x+1)^{2} - px + q \neq 0$ for all real $x$.Expanding the expression:$4x^{2} + 4x + 1 - px + q \neq 0$$4x^{2}

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(C) Given the quadratic expression is $(2x+1)^{2} - px + q \neq 0$ for all real $x$.Expanding the expression:$4x^{2} + 4x + 1 - px + q \neq 0$$4x^{2} + (4-p)x + (1+q) \neq 0$For a quadratic expression $ax^{2} + bx + c$ to be non-zero for all real $x$, its discriminant $D$ must be less than $0$.$D = b^{2} - 4ac Substituting the coefficients $a = 4$, $b = (4-p)$, and $c = (1+q)$:$(4-p)^{2} - 4(4)(1+q) $16 - 8p + p^{2} - 16 - 16q $p^{2} - 8p - 16q < 0$

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Quadratic expressions and Position of roots

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The quadratic expression $(2x+1)^{2} - px + q \neq 0$ for any real $x$, if

WBJEE 2015 All WBJEE

A
$p^{2} - 16p - 8q < 0$
B
$p^{2} - 8p + 16q < 0$
C
$p^{2} - 8p - 16q < 0$
D
$p^{2} - 16p + 8q < 0$

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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Quadratic expressions and Position of roots

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The quadratic expression $(2x+1)^{2} - px + q \neq 0$ for any real $x$, if

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