Question

Find the quadratic polynomial whose sum of roots and product of roots are 5 and 6

Answer 1

Answer:

          x² - 5x + 6

Step-by-step explanation:

For a quadratic  x² + bx + c, the sum of the roots is -b and the product of the roots is c.

To see this, notice that:

 (x - α)(x - β)  =  x² - (α+β)x + αβ

So we need:

• -b = sum of roots = 5  ⇒  b = -5
• c = product of roots = 6

Thus the quadratic that we want is

• x² - 5x + 6