(C) Let $f(x) = 2x^2 - 8x + k$.For one root to lie in $(1,2)$ and the other in $(2,3)$,the value of the quadratic at $x=2$ must be negative,and the va

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(C) Let $f(x) = 2x^2 - 8x + k$.For one root to lie in $(1,2)$ and the other in $(2,3)$,the value of the quadratic at $x=2$ must be negative,and the values at $x=1$ and $x=3$ must be positive.$f(1) = 2(1)^2 - 8(1) + k = k - 6 > 0 \implies k > 6$.$f(3) = 2(3)^2 - 8(3) + k = 18 - 24 + k = k - 6 > 0 \implies k > 6$.$f(2) = 2(2)^2 - 8(2) + k = 8 - 16 + k = k - 8 Combining these,we get $6 The only integral value of $k$ in this interval is $k = 7$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Quadratic expressions and Position of roots

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The number of integral values of $k$,for which one root of the equation $2x^2-8x+k=0$ lies in the interval $(1,2)$ and its other root lies in the interval $(2,3)$,is:

JEE MAIN 2023 All JEE MAIN

A
$2$
B
$0$
C
$1$
D
$3$

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4-2.Quadratic Equations and Inequations

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