**2.3 Forming Quadratic Equations from Given Roots**

Let

*α*and*β*be the roots of the equation*ax*^{2 }+*bx*+*c*= 0, this meansx = α or x = βx – α = 0 or x – β = 0(
x – α) (x – β) = 0So,
x^{2 }– (α + β ) x + αβ = 0Conclusion:
x^{2 }– (sum of roots) x + (product of roots) = 0 |

**Example**

**:**

Find the quadratic equation from the respective roots below:

(a) 3, −1

(a) 3, −1

(b) −2, ¼

(c) ⅔, ¼

(d) 3

(d) 3

*m*, −2*m*

*Solution:*