What is the value of x if (a + 2b – 3c)x^2 + (b + 2c – 3a)x + (c … - Vidyadip

MCQ

What is the value of x if $(\text{a} + 2\text{b} – 3\text{c})\text{x}^2 + (\text{b} + 2\text{c} – 3\text{a})\text{x} + (\text{c} + 2\text{a} – 3\text{b}) = 0$ where a, b, c are in A.P?

A
$\frac{1}{2}$
✓
$\frac{1}{4}$
C
$\frac{2}{3}$
D
$\frac{3}{4}$

✓

Answer

Correct option: B.

$\frac{1}{4}$

If the coefficients of $ (\text{x}^2 +\text{x} +\text{c}) = 0,$ then
x will always be = 1
Therefore, here, $(\text{a} + 2\text{b} – 3\text{c}) + (\text{b} + 2\text{c} – 3\text{a}) + (\text{c} + 2\text{a} – 3\text{b}) = 0$
So, x = 1.
As, one of its root is 1 so, we will calculate the other one.
As, a, b, c are in A.P so,
$\text{b}=\Big(\frac{\text{a}+\text{c}}{2}\Big)$
Thus, product of the roots $\alpha\beta =\frac{(\text{c} + 2\text{a} – 3\text{b})}{(\text{a} + 2\text{b} – 3\text{c})}$
As, a root say $\alpha=1$ then,
$\beta=\frac{\Big(\frac{\text{c}+2\text{a}-3(\text{a}+\text{c})}{2}\Big)}{\Big(\frac{\text{a}+2(\text{a}+\text{c})}{2-3\text{c}}\Big)}$
We get the value of $\beta=\frac{1}{4}$

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 COMPLEX NUMBERS AND QUADRATIC EQUATIONS→COMPLEX NUMBERS AND QUADRATIC EQUATIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

For a sequence $ < {a_n} > ,\;{a_1} = 2$ and $\frac{{{a_{n + 1}}}}{{{a_n}}} = \frac{1}{3}$. Then $\sum\limits_{r = 1}^{20} {{a_r}} $ is

The sides of a rhombus $ABCD$ are parallel to the lines, $x - y + 2\, = 0$ and $7x - y + 3\, = 0$. If the diagonals of the rhombus intersect at $P( 1, 2)$ and the vertex $A$ ( different from the origin) is on the $y$ axis, then the ordinate of $A$ is

In a survey of $220$ students of a higher secondary school, it was found that at least $125$ and at most $130$ students studied Mathematics; at least $85$ and at most $95$ studied Physics; at least $75$ and at most $90$ studied Chemistry; $30$ studied both Physics and Chemistry; $50$ studied both Chemistry and Mathematics; $40$ studied both Mathematics and Physics and $10$ studied none of these subjects. Let $\mathrm{m}$ and $\mathrm{n}$ respectively be the least and the most number of students who studied all the three subjects. Then $\mathrm{m}+\mathrm{n}$ is equal to .............................

Which of the following is a statement?

If f : R → R is defined by f(x) = 3x + |x|, then f(2x) - f(-x) - 6x =

The eccentricity of the ellipse $ (x - 3)^2 + (y - 4)^2 =$ $\frac{{{y^2}}}{9}\,$ is

On the ellipse $4{x^2} + 9{y^2} = 1$, the points at which the tangents are parallel to the line $8x = 9y$ are

If the S.D. of a set of observations is 8 and if each observation is divided by −2, the S.D. of the new set of observations will be:

Selection of menu, food, clothes, subjects, the team are examples of combinations:

A point moves in such a way that the sum of square of its distance from the points $A(2,0)$ and $B( - 2,0)$ is always equal to the square of the distance between $A$ and $B$. The locus of the point is