Question

Find polynomials when zeroes are 2,3

Answer 1

Answer:

the formula of finding polynomial is :-

x² - ( sum of zeros ) x + ( product of zeros ).

therefore the polynomial will be :-

x² - 5 x + 6 .

Answer 2

Answer:

x² - 5x + 6

Note:

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

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

★ A quadratic polynomial can have atmost two zeros .

★ If A and B are the zeros of the given quadratic polynomial ax² + Bx + C , then ;

• Sum of zeros , (A+B) = -b/a

• Product of zeros , (A•B) = c/a

★ If A and B are the zeros of any quadratic polynomial , then that quadratic polynomial is given by ; x² - (A+B)x + A•B .

Solution:

Here,

It is given that , x = 2 , 3 are the zeros of the required quadratic polynomial .

Thus,

Let A = 2 and B = 3 .

Now,

Sum of zeros of the required quadratic polynomial will be ;

A + B = 2 + 3 = 5

Also,

Product of zeros of the required quadratic polynomial will be ;

A•B = 2•3 = 6

Thus,

The required quadratic polynomial will be given as ; x² - (A+B)x + A•B

ie ; x² - 5x + 6 .

Hence,

Required answer is (x² - 5x + 6) .