Class 11Mathematics4-2.Quadratic Equations and InequationsQuadratic expressions and Position of roots
MediumIf $b > a$,then in which interval do the roots of the equation $(x - a)(x - b) - 1 = 0$ lie?
- ABoth roots in $[a, b]$
- BBoth roots in $(-\infty, a)$
- CBoth roots in $(b, +\infty)$
- DOne root in $(-\infty, a)$ and the other in $(b, +\infty)$
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Similar Questions
Number of integral values of $a$ for which the smaller root of the quadratic equation $x^2 - 2ax + a^2 - 4 = 0$ is smaller than $1$ and the bigger root is greater than $6$ is:
If $a, b, c$ are real numbers and $a > 0$,what is the minimum value of the quadratic expression $ax^2 + bx + c$ for real $x$?
Medium
View SolutionMatch the following quadratic expressions with their minimum values:
Quadratic expression The minimum value i) $x^2 + 4x + 6$ a) $1$ ii) $x^2 - 2x + 5$ b) $2$ iii) $x^2 + 6x + 18$ c) $4$ iv) $x^2 - 4x + 5$ d) $9$
| Quadratic expression | The minimum value |
|---|---|
| i) $x^2 + 4x + 6$ | a) $1$ |
| ii) $x^2 - 2x + 5$ | b) $2$ |
| iii) $x^2 + 6x + 18$ | c) $4$ |
| iv) $x^2 - 4x + 5$ | d) $9$ |
DifficultAP EAMCET 2017
View SolutionMatch the following: Consider the equation $x^2 + 2(a - 1)x + a + 5 = 0$. Match the real values of $a$ with the conditions on the roots of the given equation.
Column-$I$ Column-$II$ $A$. Imaginary roots $P$. $a \in (-1, 4)$ $B$. One root less than $3$ and other greater than $3$ $Q$. $a \in (-\infty, -1)$ $C$. One root less than $1$ and other greater than $3$ $R$. $a \in (-\infty, -4/3)$
| Column-$I$ | Column-$II$ |
|---|---|
| $A$. Imaginary roots | $P$. $a \in (-1, 4)$ |
| $B$. One root less than $3$ and other greater than $3$ | $Q$. $a \in (-\infty, -1)$ |
| $C$. One root less than $1$ and other greater than $3$ | $R$. $a \in (-\infty, -4/3)$ |
Difficult
View SolutionIf $\alpha$ and $\beta$ are the roots of the quadratic equation $ax^2 + bx + c = 0$ and $k$ is a real number,then the condition for $\alpha < k < \beta$ is given by:
Easy
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