Download App

Quadratic Equations — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsQuadratic Equations5 Marks
Question
Solve the following quadratic equations by factorization:
$\frac{\text{x}-1}{2\text{x}+1}+\frac{2\text{x}+1}{\text{x}-1}=\frac{5}{2},$ $\text{x}\neq-\frac{1}{2},1$
✓

Answer

$\frac{\text{x}-1}{2\text{x}+1}+\frac{2\text{x}+1}{\text{x}-1}=\frac{5}{2},$ $\text{x}\neq-\frac{1}{2},1$
$\Rightarrow\frac{(\text{x}-1)(\text{x}-1)+(2\text{x}+1)(2\text{x}+1)}{(2\text{x}+1)(\text{x}-1)}=\frac{5}{2}$
$\Rightarrow\frac{(\text{x}-1)^2+(2\text{x}+1)^2}{2\text{x}^2-2\text{x}+\text{x}-1}=\frac{5}{2}$
$\Rightarrow\frac{\text{x}^2-2\text{x}+1+4\text{x}^2+4\text{x}+1}{2\text{x}^2-\text{x}-1}=\frac{5}{2}$
$\Rightarrow\frac{5\text{x}^2+2\text{x}+2}{2\text{x}^2-\text{x}-1}=\frac{5}{2}$
[$\because$ $(a + b)^2 = a^2 + b^2 + 2ab, (a - b)^2 = a^2 + b^2 - 2ab]$
$\Rightarrow 2(5x^2 + 2x + 2) = 5(2x^2 - x - 1)$
$\Rightarrow 10x^2 + 4x + 4 = 10x^2 - 5x - 5$
$\Rightarrow 4x + 5x + 4 +5 = 0$
$\Rightarrow 9x + 9 = 0$
$\Rightarrow 9x = -9$
$\Rightarrow x = -1$
$\therefore$ x = -1 is the only root for the given equation

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 "5 Marks Questions" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time and the product of its zeros are 5, -2 and -24 respectively.
→
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to $\frac{\big(\text{a+c}\big)\big(\text{b + c - 2a}\big)}{2\big(\text{b - a}\big)}.$
→
Solve the following system of equations by the method of cross-multiplication:
$2ax + 3by = a + 2b,$
$3ax + 2by = 2a + b.$
→
In a $\triangle\text{ABC},\angle\text{B}=90^\circ,\text{AB}=24\text{cm}$ and BC = 7cm.
Find:
  1. $\sin\text{A}$
  2. $\cos\text{A}$
  3. $\sin\text{C}$
  4. $\cos\text{C}.$
→
The sum of the numerator and denominator of a fraction is 8. If 3 is added to both of the numerator and the denominator, the fraction becomes $\frac{3}{4}.$ Find the fraction.
→
In the given figure, is shown a sector $OAP$ of a circle with centre $O$, containing $\angle \theta . AB$ is perpendicular to the radius $O A$ and meets $O P$ produced at B. Prove that the perimeter of shaded region is $r\left[\tan \theta+\sec \theta+\frac{\pi \theta}{180}-1\right]$
Image
→
In the given figure, $\text{MNOP}$ is a parallelogram and $AB \| MP$. Prove that $QC \| PO.$
Image
→
Solve graphically the following system of linear equation. Also find the coordinates of the points where the lines meet axis of y.
3x + 2y = 12
5x - 2y = 4
→
The lower window of a house is at a height of 2m above the ground and its upper window is 4m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be $60^\circ$ and $30^\circ$, respectively. Find the height of the balloon above the ground.
→
Solve the following quadratic equation:
$\frac{3}{\text{x}+1}-\frac{1}{2}=\frac{2}{\text{3x}-1},$ $\text{x}\neq-1,\ \frac{1}{3}$
→