Question

5. Find a quadratic polynomial, the sum and product of whose zeros is 4 and 1 respectively​

Answer 1

Answer :

x² - 4x + 1

Note :

Note:

★ The possible values of the variable for which the polynomial becomes zero are called its zeros .

★ A quadratic polynomial can have atmost two zeros .

★ The general form of a quadratic polynomial is given as ; ax² + bx + c .

★ If α and ß are the zeros of the quadratic polynomial ax² + bx + c , then ;

• Sum of zeros , (α + ß) = -b/a

• Product of zeros , (αß) = c/a

★ If α and ß are the zeros of a quadratic polynomial , then that quadratic polynomial is given as : k•[ x² - (α + ß)x + αß ] , k ≠ 0.

Solution :

Let α and ß be the zeros of the required quadratic polynomial .

Now ,

It is given that , the sum and the product of zeros of the required quadratic are 4 and 1 respectively .

Thus ,

• Sum of zeros , (α + ß) = 4

• Product of zeros , (αß) = 1

Hence ,

The required quadratic polynomial will be given as ; k•[ x² - (α + ß)x + αß ] , k ≠ 0

ie. k•[ x² - 4x + 1 ] , k ≠ 0

If k = 1 , then the quadratic polynomial will be ; x² - 4x + 1 .