Question
Solve the following quadratic equations by factorization:
$4x^2+ abx - (a^2- b^2) = 0$
$4x^2+ abx - (a^2- b^2) = 0$
✓
Answer
We have been given
$ 4 x^2+a b x-\left(a^2-b^2\right)=0 $
$ 4 x^2+2(a+b) x-2(a-b) x-\left(a^2-b^2\right)=0 $
$ 2 x(2 x+a+b)-(a-b)(2 x+a+b)=0 $
$ (2 x-(a-b))(2 x+a+b)=0$
Therefore,
$2x - (a - b) = 0$
$2x = a - b$
$\text{x}=\frac{\text{a}-\text{b}}{2}$
or,$ 2x + a + b = 0$
$2x = -(a + b)$
$\text{x}=\frac{-(\text{a}+\text{b})}{2}$
Hence, $\text{x}=\frac{\text{a}-\text{b}}{2}$ or $\text{x}=\frac{-(\text{a}+\text{b})}{2}$
$ 4 x^2+a b x-\left(a^2-b^2\right)=0 $
$ 4 x^2+2(a+b) x-2(a-b) x-\left(a^2-b^2\right)=0 $
$ 2 x(2 x+a+b)-(a-b)(2 x+a+b)=0 $
$ (2 x-(a-b))(2 x+a+b)=0$
Therefore,
$2x - (a - b) = 0$
$2x = a - b$
$\text{x}=\frac{\text{a}-\text{b}}{2}$
or,$ 2x + a + b = 0$
$2x = -(a + b)$
$\text{x}=\frac{-(\text{a}+\text{b})}{2}$
Hence, $\text{x}=\frac{\text{a}-\text{b}}{2}$ or $\text{x}=\frac{-(\text{a}+\text{b})}{2}$
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
Construct a $\triangle\text{ABC}$ in which $AB = 6\ cm,$ $\angle\text{A}=30^\circ$ and $\angle\text{B}=60^\circ.$ Construct another $\triangle\text{AB}'\text{C}'$similar to $\triangle\text{ABC}$ with base $AB' = 8\ cm.$
→Solve the following quadratic equation:
$ a b x^2+\left(b^2-a c\right) x-b c=0 $
→$ a b x^2+\left(b^2-a c\right) x-b c=0 $
From the following frequency distribution, prepare the 'More Then Ogive'.
Also find the median.
→|
Score
|
Number of candidates
|
|
$400-450$
|
$20$
|
|
$450-500$
|
$35$
|
|
$500-550$
|
$40$
|
|
$550-600$
|
$32$
|
|
$600-650$
|
$24$
|
|
$650-700$
|
$27$
|
|
$700-750$
|
$18$
|
|
$750-800$
|
$24$
|
|
Total
|
$230$
|
A person on tour has Rs. $10800$ for his expenses. If he extends his tour by $4$ days, he has to cut down his daily expenses by Rs. $90$. Find the original duration of the tour.
→The sum of the squares of two consecutive positive even numbers is $452$. Find the numbers.
→Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
In the given figure, $D$ is the midpoint of side $B C$ and $A E \perp B C$. If $B C=a, A C=b, A B=c, E D=x, A D=p$ and $A E=h$, prove that..
$(\text{b}^2+\text{c}^2)=2\text{p}^2+\frac{1}{2}\text{a}^2$
→$(\text{b}^2+\text{c}^2)=2\text{p}^2+\frac{1}{2}\text{a}^2$
Calculate the median from the following data:
|
Marks below
|
10
|
20
|
30
|
40
|
50
|
60
|
70
|
80
|
|
No. of students
|
15
|
35
|
60
|
84
|
96
|
127
|
198
|
250
|
Two different dice are thrown together. Find the probability that the number obained have
-
Even sum.
-
Even prouduct.
Solve the following systems of equations:
$\text{x}+\text{y}=2\text{xy},$
$\frac{\text{x}-\text{y}}{\text{xy}}=6,\text{x}\neq0,\text{y}\neq0.$
→$\text{x}+\text{y}=2\text{xy},$
$\frac{\text{x}-\text{y}}{\text{xy}}=6,\text{x}\neq0,\text{y}\neq0.$