Question

find the quadratic polynomial whose zeroes are 4 and 1

Answer 1

hope this helps you......

Answer 2

Answer:

x² - 5x + 4

Step-by-step explanation:

The steps to find the quadratic polynomial are as follows:

Step 1: Find the sum of the two roots. Sum of roots = 4 + 1= 5

Step 2: Find the product of the two roots. Product of roots = 4 X 1 = 4.

Step 3: Substitute these values in the expression x² - (sum of the roots)x + (product of the roots).

Step 4: Thus, the quadratic polynomial will be x² - 5x + 4.

Note: The general form of a quadratic polynomial is ax² + bx + c.

Example:

Let the zeroes of the quadratic polynomial be α=3,β=−3 Then.

a+β=3+(−3)=0.

αβ=3×(−3)=−9.

Sum of zeroes = a+β=0.

Product of zeroes = αβ = −9.

Then, the quadratic polynomial = x²−( sum of zeroes )x+ product of zeroes

x² - 0x - 9

Or,  x² - 9