Sarvesh K Verma Solutions for Chapter: Theory of Equations, Exercise 7: Practice Exercise

If the two real roots are distinct, then which of the following may be correct?

The graph of a quadratic equation is symmetrical about Y-axis, which one of the following can't be the roots of a quadratic equation?

If the roots of a quadratic equation are ($4,10$), then what is the distance between the Y-axis and the axis of symmetry of the pertinent graph?

The distance between the Y-axis and the axis of symmetry is $4$ and one of the two roots is $-9$, then what can be the other root?

In a set of $200$quadratic equations, the discriminant D for different equations is such that $\mathrm{D}=-99,-98, 99,100$. Then which one of the following is not true?

Which one(s) of the following graphs is/are correctly sketched for the given quadratic equation which has a double root (i.e., both the roots are equal), considering that all of these graphs appear considerably thick when seen with a magnifying lens? The horizontal lines, in these graphs, represent the X-axis.

The graph of the equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ is shown below. If D denotes the discriminant of this equation; S and P, denote the sum and product of the roots of this equation, respectively. Then which of the following facts is/are true pertaining to this graph?

$\text{ (i) }\mathrm{D}<0$
$\text{ (ii) }\mathrm{a}<0$
$\text{(iii)} \mathrm{S}>0$
$\text{(iv)} \mathrm{P}<0$
$\text{ (v) }-\frac{\mathrm{b}}{\mathrm{a}}>0$
$\text{ (vi) }\frac{\mathrm{c}}{\mathrm{a}}>0$

Some facts are given below for a quadratic equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$, and then four graphs are also drawn. If D denotes the discriminant of this equation; S and P denote the sum and product of the roots of this equation, respectively, which one of the following graphs is the best representative of all these facts?

$\text{ (i) }\mathrm{D}>0$
$\text{ (ii) }\mathrm{a}<0$
$\text{ (iii) }\mathrm{S}<0$
$\text{ (iv) }\mathrm{P}<0$
$\text{ (v) }-\frac{\mathrm{b}}{\mathrm{a}}<0$
$\text{ (vi) }\frac{\mathrm{C}}{\mathrm{a}}<0$