(D) Let $f(x) = (x - a)(x - b) - 1 = 0$. $f(a) = (a - a)(a - b) - 1 = -1 < 0$. $f(b) = (b - a)(b - b) - 1 = -1 < 0$. Since $f(x)$ is a parabola openin

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One root in $(-\infty, a)$ and the other in $(b, +\infty)$

(D) Let $f(x) = (x - a)(x - b) - 1 = 0$. $f(a) = (a - a)(a - b) - 1 = -1 $f(b) = (b - a)(b - b) - 1 = -1 Since $f(x)$ is a parabola opening upwards,and $f(a) Because the parabola opens upwards and $f(a) Thus,one root lies in $(-\infty, a)$ and the other root lies in $(b, +\infty)$.

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

Medium

If $b > a$,then the equation $(x - a)(x - b) = 1$ has

IIT 2000 All IIT

A
Both roots in $[a, b]$
B
Both roots in $(-\infty, a)$
C
Both roots in $(b, +\infty)$
D
One root in $(-\infty, a)$ and the other in $(b, +\infty)$

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4-2.Quadratic Equations and Inequations

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Quadratic expressions and Position of roots

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If $b > a$,then the equation $(x - a)(x - b) = 1$ has

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