Question

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

x squared space plus space 5 x space plus space 6
x squared space plus space 6 x space plus space 6
x squared space plus space 6 x space plus space 5
none

Answer 1

Question :

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

• x² + 5 x + 6

• x² + 6 x + 6

• x² + 6 x + 5

• none

Answer :

x² + 5x + 6

Step-by-step explanation :

    $\underline{\underline{\bf Quadratic \ polynomial :}}}$

          ✯ It is a polynomial of degree 2

          ✯ General form :

                    ax² + bx + c

          ✯ 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 = -5

   => Product of roots = 6

Required quadratic polynomial is of the form :

     $\boxed{\bf x^{2} - \textbf{(sum of zeroes)x+(product of zeroes)}}$

     $\implies x^{2} -(-5)x+6 \\\\ \implies x^{2} +5x+6$

Answer 2

Answer:

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

x² + 5 x + 6

x² + 6 x + 6

x² + 6 x + 5

none

Answer :

x² + 5x + 6

Step-by-step explanation :