If x is real- y-x 2-3 x-4 x 2-3 x-4- then y will lie between-A- 17 and 7B- -1 and 1C- 15 and 5D- -3 and 3

The correct option is A 17 nbsp;and nbsp;7y=x2 3x+4x2+3x+4⇒x2(y 1)+3x(y+1)+4(y 1)=0If nbsp;x nbsp;is nbsp;real nbsp;⇒ nbsp;D≥0⇒9(y+1)2 16(y 1)2≥0⇒ ...

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Byju's Answer

Standard XII

Mathematics

Range of Quadratic Expression

If x is real,...

Question

If x is real, y=x2−3x+4x2+3x+4, then y will lie between .

\frac{1}{7} a n d 7

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-1 and 1

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\frac{1}{5} a n d 5

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-3 and 3

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Solution

The correct option is A $\frac{1}{7} a n d 7$
$y = \frac{x^{2} - 3 x + 4}{x^{2} + 3 x + 4} \Rightarrow x^{2} (y - 1) + 3 x (y + 1) + 4 (y - 1) = 0 I f x i s r e a l \Rightarrow D \geq 0 \Rightarrow 9 (y + 1)^{2} - 16 (y - 1)^{2} \geq 0 \Rightarrow - 7 y^{2} + 50 y - 7 \geq 0 \Rightarrow 7 y^{2} - 50 y + 7 \leq 0 \Rightarrow (7 y - 1) (y - 7) \leq 0 \Rightarrow \frac{1}{7} \leq y \leq 7$

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If x is real, y=x2−3x+4x2+3x+4, then y will lie between .

The correct option is A 17 and 7y=x2−3x+4x2+3x+4⇒x2(y−1)+3x(y+1)+4(y−1)=0If x is real ⇒ D≥0⇒9(y+1)2−16(y−1)2≥0⇒−7y2+50y−7≥0⇒7y2−50y+7≤0⇒(7y−1)(y−7)≤0⇒17≤y≤7