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:

Start with the quadratic equation and distribute the terms to expand the equation.
Now on solving, notice the common factor and factor it out and simplify further.
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.

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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

Answer:

x=a and x=1/a are the Zeros of Quadratic Equation a(x²+1)-x(a²+1)=0

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