Question
Solve the following quadratic equations by factorization:
$ax^2 + (4a^2 - 3b)x - 12ab = 0$
$ax^2 + (4a^2 - 3b)x - 12ab = 0$
✓
Answer
We have,
$a x^2+\left(4 a^2-3 b\right) x-12 a b=0$
${\left[a \times 12 a b=-12 a^2 b^2=4 a^2 x-3 b\right]}$
$\Rightarrow a x^2+4 a^2 x-3 b x+(4 a \times(-3 b))=0$
$\Rightarrow a x(x+4 a)-3 b(x+4 a)=0$
$\Rightarrow(x+4 a)(a x-3 b)=0$
$\Rightarrow(x+4 a)=0 \text { or }(a x-3 b)=0$
$\Rightarrow x=-4 a \text { or } x=\frac{3 b}{a}$
$\therefore x =\frac{3 b}{ a }$ and $x =-4 a$ are the two roots of the given equations.
$a x^2+\left(4 a^2-3 b\right) x-12 a b=0$
${\left[a \times 12 a b=-12 a^2 b^2=4 a^2 x-3 b\right]}$
$\Rightarrow a x^2+4 a^2 x-3 b x+(4 a \times(-3 b))=0$
$\Rightarrow a x(x+4 a)-3 b(x+4 a)=0$
$\Rightarrow(x+4 a)(a x-3 b)=0$
$\Rightarrow(x+4 a)=0 \text { or }(a x-3 b)=0$
$\Rightarrow x=-4 a \text { or } x=\frac{3 b}{a}$
$\therefore x =\frac{3 b}{ a }$ and $x =-4 a$ are the two roots of the given equations.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find four numbers in AP whose sum is $28$ and the sum of whose squares is $216$.
→Two customers are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on:
- The same day?
- Different days?
- Consecutive days?
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
The following table shows the classification of percentages of marks of students and the number of students. Draw a frequency polygon from the table.
| Result (Percentage) | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of students | 7 | 33 | 45 | 65 | 47 | 18 | 5 |
In the given figure, $\angle\text{B}<90^\circ$ and segment $\text{AD}\perp\text{BC}$ show that
→
- $b^2 = h^2 + a^2 + x^2 - 2ax$
- $b^2 = a^2 + c^2 - 2ax$
A number consist of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.
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.
→The semi perimeter of a rectangular shape garden is 36 m. The length of the garden is 4 m more than its breadth. Find the length and the breadth of the garden.
Ranjana wants to distribute 540 oranges among some students. If 30 students were more each would get 3 oranges less. Find the number of students.
Show taht the following points are collinear:$A(-5, 1), B(5, 5)$ and $C(10, 7)$
→