Question

find a quadratic polynomial,the sum and product of whose zeroes are -5 and 6 respectively​

Answer 1

hey there!!!

Solution:

let the zeroes if the polynomial be a and B... ( a= alpha, B= Beta)

now,

a+B= -5.... sum..... (1)

a×B= 6........product.....(2)

we know,

the formula for finding a quadratic polynomial=

x^2-(a+B)x+aB= 0

x^2-(-5)x+6= 0

x^2+5x+6= 0.........required quadratic polynomial

hope this helps!!!

Answer 2

Answer:

The required quadratic polynomial with sum and product of zeroes are -5 and 6 respectively is  x^2 + 5x+ 6 = 0.

Step-by-step explanation:

• Let  and b are two zeroes of a polynomial

           then the quadratic polynomial can be written as

                x^2 - (sum of zeroes )x + (product of zeroes) = 0

                                            x^2-(a+b)x + (ac) = 0  ----------------(i)

• Given

              Sum of zeroes   = (a+b) = -5

            Product of zeroes = ab = 6

        Substitute the above values in equation (i)

                     x^2 - (-5x)+ 6 = 0  

                        x^2 + 5x+ 6 = 0

  Hence the quadratic polynomial is  x^2 + 5x+ 6 = 0

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