(D) Let $y = \frac{2(x^2+2x-11)}{2x-5}$.$y(2x-5) = 2x^2+4x-22$.$2x^2 + x(4-2y) + (5y-22) = 0$.Since $x$ is real,the discriminant $D \geq 0$.$D = (4-2y

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(D) Let $y = \frac{2(x^2+2x-11)}{2x-5}$.$y(2x-5) = 2x^2+4x-22$.$2x^2 + x(4-2y) + (5y-22) = 0$.Since $x$ is real,the discriminant $D \geq 0$.$D = (4-2y)^2 - 4(2)(5y-22) \geq 0$.$16 + 4y^2 - 16y - 40y + 176 \geq 0$.$4y^2 - 56y + 192 \geq 0$.$y^2 - 14y + 48 \geq 0$.$(y-6)(y-8) \geq 0$.Thus,$y \in (-\infty, 6] \cup [8, \infty)$.Therefore,no value of the expression lies in the interval $(6,8)$.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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If $x$ is real,then the interval in which no value of the expression $\frac{2(x^2+2x-11)}{2x-5}$ lies,is

TS EAMCET 2019 All TS EAMCET

A
$(2,5)$
B
$(3,6)$
C
$(3,4)$
D
$(6,8)$

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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Solution of quadratic equations and Nature of roots

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