Question

find a quadratic polynomial the sum and product of whose zeroes are -3and 2 respectively​

Answer 1

Answer:

Given, Sum of Zeroes = - 3

alpha  +  beta  =  - 3

Product of Zeroes = 2

alpha  beta  = 2

Quadratic polynomial is

k {x}^{2}  - (sum \:  \: of \:  \: zeroes) + (product \:  \: of \:  \: zeroes)

k {x}^{2}  - ( - 3) + (2)

k {x}^{2}  + 3 +2

k = 1

{x}^{2}  + 3 + 2

Step-by-step explanation:

Answer 2

Answér :

x² + x - 6

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.

★ The discriminant , D of the quadratic polynomial ax² + bx + c is given by ;

D = b² - 4ac

★ If D = 0 , then the zeros are real and equal .

★ If D > 0 , then the zeros are real and distinct .

★ If D < 0 , then the zeros are unreal (imaginary) .

Solution :

Here ,

It is given that , -3 and 2 are the zeros of the required quadratic polynomial .

Thus ,

Let α = -3 and ß = 2

Now ,

Sum of zeros of the required quadratic polynomial will be ;

α + ß = -3 + 2 = -1

Also ,

Product of zeros of the required quadratic polynomial will be ;

αß = -3×2 = -6

Thus ,

The required quadratic polynomial polynomial will be ;

=> k•[ x² - (α + ß)x + αß ]

=> k•[ x² - (-1)x + (-6) ]

=> k•[ x² + x - 6 ]

For k = 1 , the polynomial will be ;

x² + x - 6

Hence ,

Required answer is : x² + x - 6