Question

the quadratic polynomial for which the sum and the product of zeroes are 11 and 28 respectively is​

Answer 1

Answer:

The required quadratic polynomial is x² – 11x + 28.

Step-by-step explanation:

About Quadratic Polynomial :

✯ 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

________________________________

Given,

Sum of zeroes = 11

Product of zeroes = 28

To find :

the quadratic polynomial

Solution :

The quadratic polynomial is of the form

x² – (sum of zeroes)x + (product of zeroes)

So,

x² – 11x + 28 is the required Quadratic Polynomial.

Answer 2

$\alpha + \beta = 11$

$\alpha \beta = 28$

so ,

$\orange{ \sf {x}^{2} + ( \alpha + \beta )x - \alpha \beta }$

so ,

x² + (11)x - 28

⇒ x² + 11x - 28