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

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.

Answer:

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

Similar Questions:

• Find the Zeros of the Quadratic Polynomial 4u²+8u and Verify the Relationship between the Zeros and the Coefficient
• If sum of the Zeros of the Polynomial Ky^2+2y-3K is Twice their product of Zeros then Find the Value of K
• If α and β are the Zeros of the Polynomial f(x)=x^2+x−2, Find the Value of (1/α−1/β)
• If α and β are the Zeros of the Quadratic Polynomial f(x) = ax^2 + bx + c, then Evaluate
• If α and β are the Zeros of the Quadratic Polynomial p(x) = 4x^2 − 5x − 1, Find the Value of α^2β + αβ^2
• If 1 is the Zero of the Polynomial p(x) = ax² – 3(a – 1) x – 1, Then Find the Value of a