  # Solve the Quadratic Equation by Factorization: a(x²+1)-x(a²+1)=0

By BYJU'S Exam Prep

Updated on: October 17th, 2023 x = 1/a and x = a are the zero of quadratic equation a(x2+1)-x(a2+1)=0

Here are the step-by-step instructions to solve the quadratic equation a(x2+1)-x(a2+1)=0 by factorization and to reach the above mentioned result:

2. Now on solving, notice the common factor and factor it out and simplify further.
3. After further solving, we will get factored the equation as a product of two terms. To find the values of, we set each factor equal to zero andd solve.

Table of content ## Solve the Quadratic Equation by Factorization: a(x²+1)-x(a²+1)=0

Solution:

Let’s solve the quadratic equation ax²-(a²+1)x+a=0 correctly:

To solve the equation, we’ll factorize it:

ax²-(a²+1)x+a=0

Rearranging the terms:

ax²-ax-a²x+a=0

Grouping the terms:

ax²-a²x-ax+a=0

Factoring by grouping:

ax(x-a)-(x-a)=0

Now, we can factor out the common factor of (x-a):

(x-a)(ax-1)=0

Setting each factor equal to zero:

x-a=0 or ax-1=0

If x-a=0, we have x=a.

ax-1=0, we can solve for x:

ax=1

Dividing both sides by a:

x=1/a

Therefore, the solutions to the quadratic equation ax²-(a²+1)x+a = 0 are x=a and x=1/a GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 help@byjusexamprep.com