Download App

Quadratic Equations — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsQuadratic Equations4 Marks
Question
Solve the following quadratic equations by factorization:
$\frac{\text{m}}{\text{n}}\text{x}^2+\frac{\text{n}}{\text{m}}=1-2\text{x}$
✓

Answer

We have been given
$\Rightarrow\frac{\text{m}}{\text{n}}\text{x}^2+\frac{\text{n}}{\text{m}}=1-2\text{x}$
$\Rightarrow\frac{\text{m}^2\text{x}^2+\text{n}^2}{\text{mn}}=1-2\text{x}$
$\Rightarrow\text{m}^2\text{x}^2+2\text{mnx}+(\text{n}^2-\text{mn})=0$
$\Rightarrow\text{m}^2\text{x}^2+\text{mnx}+\text{mnx}+\big[\text{n}^2-(\sqrt{\text{mn}})^2\big]=0$
$\Rightarrow\text{m}^2\text{x}^2+\text{mnx}+\text{mnx}+(\text{n}+\sqrt{\text{mn}})(\text{n}-\sqrt{\text{mn}})\\+(\text{m}\sqrt{\text{mnx}}-\text{m}\sqrt{\text{mnx}})=0$
$\Rightarrow\big[\text{m}^2\text{x}^2+\text{mnx}+\text{m}\sqrt{\text{mnx}}\big]+\big[\text{mnx}-\text{m}\sqrt{\text{mnx}}\\+(\text{n}+\sqrt{\text{mn}})(\text{n}-\sqrt{\text{mn}})\big]=0$
$\Rightarrow\big[\text{m}^2\text{x}^2+\text{mnx}+\text{m}\sqrt{\text{mnx}}\big]+\big[(\text{mx}(\text{n}-\sqrt{\text{mn}})\\+(\text{n}+\sqrt{\text{mn}})(\text{n}-\sqrt{\text{mn}})\big]=0$
$\Rightarrow(\text{mx})\big(\text{mx}+\text{n}+\sqrt{\text{mn}}\big)+\big(\text{n}-\sqrt{\text{mn}}\big)\\\big(\text{mx}+\text{n}+\sqrt{\text{mn}}\big)=0$
$\Rightarrow\big(\text{mx}+\text{n}+\sqrt{\text{mn}})\big(\text{mx}+\text{n}-\sqrt{\text{mn}}\big)=0$
Therefore,
$\Rightarrow\text{mx}+\text{n}+\sqrt{\text{mn}}=0$
$\Rightarrow\text{mx}=-\text{n}-\sqrt{\text{mn}}$
$\Rightarrow\text{x}=\frac{-\text{n}-\sqrt{\text{mn}}}{\text{m}}$
or, $\text{mx}+\text{n}-\sqrt{\text{mn}}=0$
$\Rightarrow\text{mx}=-\text{n}+\sqrt{\text{mn}}$
$\Rightarrow\text{x}=\frac{-\text{n}+\sqrt{\text{mn}}}{\text{m}}$
Hence, $\text{x}=\frac{-\text{n}-\sqrt{\text{mn}}}{\text{m}}$ or $\text{x}=\frac{-\text{n}+\sqrt{\text{mn}}}{\text{m}}$

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

Similar questions

Two water taps together can fill a tank in $9\frac{3}{8}$ hours. The of larger diameter takes $10$ hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
→
If (3y - 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
→
Evaluate the following:
If A = 60° and B = 30°, verify that:
$\sin(\text{A}-\text{B})=\sin\text{A}\cos\text{B}-\cos\text{A}\sin\text{B}$
→
Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is $800m^2$?
​​​​​​​If so, find its length and breadth.
→
The corresponding altitudes of two similar triangles are 6cm and 9cm respectively. Find the ratio of their areas.
→
Draw a $\triangle ABC$ in which $BC = 6\ cm, AB = 4\ cm$ and $AC = 5\ cm$.
Draw a triangle similar to $\triangle\text{ABC}.$
with its sides equal to $\Big(\frac{3}{4}\Big)^\text{th}$ of the corresponding sides of $\triangle\text{ABC}.$
→
Show that A (-4, -7),B (-1, 2), C (8, 5) and D (5, -4) are the vertices of a parallelogram.
→
Solve the following systems of equations:
$\frac{15}{\text{u}}+\frac{2}{\text{v}}=17$
$\frac{1}{\text{u}}+\frac{1}{\text{v}}=\frac{36}{5}$
→
$300$ apples are distributed equally among a certain number of students. Had there been $10$ more students, each would have received one apple less. Find the number of students.
→
A number consist of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.
→