If the roots of the equation a x^2 + bx + c = 0be and , then the … - Vidyadip

MCQ

If the roots of the equation $a{x^2} + bx + c = 0$be $\alpha $and $\beta $, then the roots of the equation $c{x^2} + bx + a = 0$ are

A
$ - \alpha , - \beta $
B
$\alpha ,\frac{1}{\beta }$
✓
$\frac{1}{\alpha },\frac{1}{\beta }$
D
None of these

✓

Answer

Correct option: C.

$\frac{1}{\alpha },\frac{1}{\beta }$

c
(c) $\alpha ,\beta $are roots of $a{x^2} + bx + c = 0$

==> $\alpha + \beta = - \frac{b}{a}$ and $\alpha \beta = \frac{c}{a}$

Let the roots of $c{x^2} + bx + a = 0$be $\alpha ',\beta '$, then

$\alpha ' + \beta ' = - \frac{b}{c}$and $\alpha '\beta ' = \frac{a}{c}$

but $\frac{{\alpha + \beta }}{{\alpha \beta }} = \frac{{ - b/a}}{{c/a}} = \frac{{ - b}}{c}$

==>$\frac{1}{\alpha } + \frac{1}{\beta } = \alpha ' + \beta '$

Hence $\alpha ' = \frac{1}{\alpha }$ and $\beta ' = \frac{1}{\beta }$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 4.2 Quadratic equations and inequations→4.2 Quadratic equations and inequations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

At what point on the parabola ${y^2} = 4x$, the normal makes equal angles with the co-ordinate axes

If (a, b) lies on circle with centre as origin, then its radius will be:

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after:

Coefficients of ${x^r}[0 \le r \le (n - 1)]$ in the expansion of ${(x + 3)^{n - 1}} + {(x + 3)^{n - 2}}(x + 2)$$ + {(x + 3)^{n - 3}}{(x + 2)^2} + ... + {(x + 2)^{n - 1}}$

If the functions are defined as $f(x)=\sqrt{x}$ and $g ( x )=\sqrt{1- x },$ then what is the common domain of the following functions: $f+g, f-g, f / g, g / f, g-f$ where $(f \pm g)(x)=$ $f(x) \pm g(x),(f / g)(x)=\frac{f(x)}{g(x)}$

Jairam purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual instalment of Rs. 1000 with 10% per annum interest. How much money is to be paid by Jairam?

Let $f(x)={{x}^{2}}-x+k-2,k\in R$ then the complete set of values of $k$ for which $y=\left| f\left( \left| x \right| \right) \right|$ is non-derivable at $5$ distinict points is

The locus of the mid-points of the perpendiculars drawn from points on the line, $\mathrm{x}=2 \mathrm{y}$ to the line $\mathrm{x}=\mathrm{y}$ is

Consider the lines $L_1$ and $L_2$ defined by

$L _1: x \sqrt{2}+ y -1=0$ and $L _2: x \sqrt{2}- y +1=0$

For a fixed constant $\lambda$, let $C$ be the locus of a point $P$ such that the product of the distance of $P$ from $L_1$ and the distance of $P$ from $L_2$ is $\lambda^2$. The line $y=2 x+1$ meets $C$ at two points $R$ and $S$, where the distance between $R$ and $S$ is $\sqrt{270}$.

Let the perpendicular bisector of $RS$ meet $C$ at two distinct points $R ^{\prime}$ and $S ^{\prime}$. Let $D$ be the square of the distance between $R ^{\prime}$ and $S ^{\prime}$.

($1$) The value of $\lambda^2$ is

($2$) The value of $D$ is

Let $L_1, L_2$ be the lines passing through the point $\mathrm{P}(0,1)$ and touching the parabola $9 x^2+12 x+18 y-14=0$. Let $Q$ and $R$ be the points on the lines $\mathrm{L}_1$ and $\mathrm{L}_2$ such that the $\triangle \mathrm{PQR}$ is an isosceles triangle with base $\mathrm{QR}$. If the slopes of the lines $Q R$ are $m_1$ and $m_2$. then $16\left(m_1^2+m_2^2\right)$ is equal to ..............