Question

find a quadratic Polynomial whose zeroes are
3 and -l​

Answer 1

Answer :

The required quadratic polynomial is x² - 2x - 3

Step-by-step explanation :

Given zeroes are 3 and -1,

➙ Sum of zeroes

         = 3 + (-1)

         = 3 - 1

         = 2

➙ Product of zeroes

         = 3(-1)

         = -3

The quadratic polynomial is of the form :

⇝ x² - (sum of zeroes)x + (product of zeroes)

Substituting the values of sum and product of zeroes,

x² - (2)x + (-3)

x² - 2x - 3

The required quadratic polynomial is x² - 2x - 3

--------------------------------------------

About Quadratic Polynomials :

✯ It is a polynomial of degree 2

✯ General form :

   ax² + bx + c  = 0

✯ Determinant, D = b² - 4ac

✯ Based on the value of Determinant, we can define the nature of roots.

 D > 0 ; real and unequal roots

 D = 0 ; real and equal roots

 D < 0 ; no real roots i.e., imaginary

✯ Relationship between zeroes and coefficients :

  ✩ Sum of zeroes = -b/a

  ✩ Product of zeroes = c/a

________________________________

Answer 2

$\sf{Answer}$

Step by step explanation:-

We have to find the Quadratic polynomial whose zeros are 3, -1

Quadratic polynomial = x²-(Sum of roots)x + product of roots

So, Sum of zeroes = 3 +(-1) = 3-1

Sum of zeroes = 2

Product of zeros = 3 ×-1

Product of zeroes= -3

Hence Required polynomial is

x² -(sum of roots)x+ product of roots

x² -(2)x +(-3)

x² -2x -3 is Required polynomial

Hence this Quadratic equation has roots of 3,-1

Verification:-

x²-2x-3=0

x² -3x +x -3 =0

x(x-3)+1(x-3)=0

(x-3)(x+1)=0

x = 3,-1 Hence verified

Similar questions in brainly

https://brainly.in/question/33000182?utm_source=android&utm_medium=share&utm_campaign=question