Find the range of rational expression y -x2-34 x-71-x2-2 x-7 if x is realA- - ndash- 5-9-B- -5-9- C- - 5- -9- -D- -5- -9- -

The correct option is C y = x^2+34x 71/x^2+2x 7⇒ x^2 (y 1)+x(2y 34)+(71 7y)=0 Given that x is real ⇒ b^2 4ac ≥ 0 ⇒ (2y 34)^2 4(y 1)(71 7y)≥ 0 4 [ y^2+289 ...

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Byju's Answer

Standard XII

Mathematics

Range of Quadratic Expression

Find the rang...

Question

Find the range of rational expression $y = \frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}$ if x is real

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Solution

The correct option is C

$y = \frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}$ $\Rightarrow x^{2} (y - 1) + x (2 y - 34) + (71 - 7 y) = 0$

Given that x is real

$\Rightarrow b^{2} - 4 a c \geq 0 \Rightarrow (2 y - 34)^{2} - 4 (y - 1) (71 - 7 y) \geq 0 4 [y^{2} + 289 - 34 y + 7 y^{2} - 78 y + 71] \geq 0 y^{2} - 14 y + 45 \geq 0 y (y - 9) - 5 (y - 9) \geq 0 (y - 5) (y - 9) \geq 0$

$f o r y \leq 5 & y \geq 9 y \leq 5 a n d y \geq 9 H e n c e y ϵ (- \infty, 5] \cup [9, \infty)$

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Similar questions

find the range of rational expression $y = \frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}$ if x is real

Find the range of rational expression $y = \frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}$ if x is real

Q. For x

\in

R, the range of the given expression

\frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}

Q. The given expression

\frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}

lies in the range

Q. Show that the values of the function

\frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}

do not lie between

5

and

9

for all,

x \in R

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Find the range of rational expression y=x2+34x−71x2+2x−7 if x is real

Find the range of rational expression $y = \frac{x^{2} + 34 x - 71}{x^{2} + 2 x - 7}$ if x is real