# What Should be Added to the Quadratic Polynomial x²-5x+4 so that 3 is a Zero of the Resulting Polynomial?

By BYJU'S Exam Prep

Updated on: October 17th, 2023

What should be added to the quadratic polynomial x²-5x+4 so that 3 is a zero of the resulting polynomial?

To solve the given problem, we will first denote the unknown value to be added as c. The new polynomial would be (x² – 5x + 4) + c. Set up the equation (x² – 5x + 4) + c = 0, as we want the resulting polynomial to evaluate to zero when x = 3.

Substitute x = 3 into the equation and simplify the equation to solve for c by isolating it on one side of the equation.

## What Should be Added to the Quadratic Polynomial x²-5x+4 so that 3 is a Zero of the Resulting Polynomial?

Solution:

To make 3 a zero of the resulting polynomial, we need to find the value to add to the quadratic polynomial x² – 5x + 4 such that when x = 3, the resulting polynomial evaluates to zero.

Let’s denote the unknown value as c. Therefore, the new polynomial would be (x² – 5x + 4) + c.

We know that when x = 3, the resulting polynomial should equal zero. So, we can set up the equation:

(3² – 5(3) + 4) + c = 0

Simplifying this equation:

(9 – 15 + 4) + c = 0

(-2) + c = 0

c = 2

Therefore, to make 3 a zero of the resulting polynomial, we need to add 2 to the quadratic polynomial x² – 5x + 4. The resulting polynomial would be x² – 5x + 6.