If x−px2−3x+2 takes all real values for x∈R, then the range of P is

y=x−px2−3x+2yx2−3yx+2y−x+p=0 yx2−(3y+1)x+2y+p=0 Δ≥0⇒(3y+1)2−4(y)(2y+p)≥0⇒Again Δ<0⇒1<P<2

If x−px2−3x+2 takes all real values for x∈R, then the range of P is

y=x−px2−3x+2yx2−3yx+2y−x+p=0 yx2−(3y+1)x+2y+p=0 Δ≥0⇒(3y+1)2−4(y)(2y+p)≥0⇒Again Δ<0⇒1<P<2

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If $\frac{x - p}{x^{2} - 3 x + 2}$ takes all real values for $x \in R$ , then the range of P is

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$1 \leq p \leq 2$

$1 < p < 2$

$p < 1 (o r) p > 2$

None

answer is B.

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$y = \frac{x - p}{x^{2} - 3 x + 2}$

$y x^{2} - 3 y x + 2 y - x + p = 0$

$y x^{2} - (3 y + 1) x + 2 y + p = 0$

$Δ \geq 0$

$\Rightarrow (3 y + 1)^{2} - 4 (y) (2 y + p) \geq 0$

$\Rightarrow Again Δ < 0 \Rightarrow 1 < P < 2$

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If x−px2−3x+2 takes all real values for x∈R, then the range of P is

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If $\frac{x - p}{x^{2} - 3 x + 2}$ takes all real values for $x \in R$ , then the range of P is