(D) For a quadratic expression $P(x) = ax^2+bx+c$ to be positive for all real values of $x$,the conditions are $a>0$ and the discriminant $D < 0$.Here

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(D) For a quadratic expression $P(x) = ax^2+bx+c$ to be positive for all real values of $x$,the conditions are $a>0$ and the discriminant $D Here,$a=1$,which is $>0$.Now,calculate the discriminant $D = b^2-4ac $D = (2p)^2 - 4(1)(-2p+8) $4p^2 + 8p - 32 Divide by $4$:$p^2 + 2p - 8 Factor the quadratic:$(p+4)(p-2) For the product to be negative,$p$ must lie between the roots:$p \in (-4, 2)$

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

If $x^2+2px-2p+8>0$ for all real values of $x$,then the set of all possible values of $p$ is

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$(2,4)$
B
$(-\infty,-4)$
C
$(2, \infty)$
D
$(-4,2)$

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If $x^2+2px-2p+8>0$ for all real values of $x$,then the set of all possible values of $p$ is

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