Question
Solve the following quadratic equations by factorization:
$x^2 + 2ab = (2a + b)x$
$x^2 + 2ab = (2a + b)x$
✓
Answer
We have
$x^2 + 2ab = (2a + b)x$
$\Rightarrow x^2 - (2a + b)x + 2ab = 0$
[$\because$ $2ab = -8a \times -b \Rightarrow -(8a + b) = -8a - b$
$\Rightarrow x^2 - 2ax - bx + 2ab = 0$
$\Rightarrow x - (x - 8a) - b(x - 2a) = 0$
$\Rightarrow (x - 8a)(x - b) = 0$
$\Rightarrow x - 8a = 0$ or$ x - b = 0$
$\Rightarrow x = 8a = 0$ or $x = b$
$\therefore$ $x = 8a$ and $x = b$ are the two roots of the given equation.
$x^2 + 2ab = (2a + b)x$
$\Rightarrow x^2 - (2a + b)x + 2ab = 0$
[$\because$ $2ab = -8a \times -b \Rightarrow -(8a + b) = -8a - b$
$\Rightarrow x^2 - 2ax - bx + 2ab = 0$
$\Rightarrow x - (x - 8a) - b(x - 2a) = 0$
$\Rightarrow (x - 8a)(x - b) = 0$
$\Rightarrow x - 8a = 0$ or$ x - b = 0$
$\Rightarrow x = 8a = 0$ or $x = b$
$\therefore$ $x = 8a$ and $x = b$ are the two roots of 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.
Explore more
Similar questions
In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6cm, BC = 7cm and CD = 4cm. Find AD. 
Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:
$5x^2 - 4 - 8x$
→$5x^2 - 4 - 8x$
A solid cylinder of diameter 12cm and height 15cm is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3cm.If the height of the toy is 12cm, find the number of toys so formed.
If the coordinates of the mid-points of the sides of a triangle are $(1, 1) (2, -3)$ and $(3, 4)$, find the vertices of the triangle.
→Solve the following quadratic equation:$\frac{2}{\text{x}^2}-\frac{5}{\text{x}}+2=0$
→In the seating arrangement of desks in a classroom three students Rohini, Sandhya and Bina are seated at A(3, 1), B(6, 4) and C(8, 6). Do you think they are seated in a line?
The slant height of the frustum of a cone is $5\ cm$. If the difference between the radii of its two circular ends is $4\ cm$, write the height of the frustum.
→Find the common difference and write the next four terms of the following arithmetic progressions:
$0,-3,-6,-9, \ldots . .$
→$0,-3,-6,-9, \ldots . .$
$\triangle X Y Z \sim \Delta ABC , \angle X=40^{\circ}, \angle Y=80^{\circ}, X Y=6 cm$. Draw $\triangle ABC$, if $AB : XY =3: 2$
→The radii of two cylinders are in the ratio $3 : 5$ and their heights are in the ratio $2 : 3$. What is the ratio of their curved surface areas?
→