Question
Find the quadratic polynomial whose zeros are 2 and -6. Verify the relation between the coeficients and the zeros of the polynomial.
✓
Answer
Let $\alpha =2$ and $\beta=-6$
Sum of the zeros $=(\alpha+\beta)$
$=2+(-6) =- 4$
Product of the zeros $=\alpha\beta$
$=2\times(-6) =- 12$
$\therefore$ Required polynomial $=\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$=\text{x}^2-(-4)\text{x}-12$
$=\text{x}^2+\text{4x}-12$
Sum of the zeros = -4
$=\frac{-4}{1}=\frac{-(\text{Coefficient of x})}{(\text{Coefficient of }\text{x}^2)}$
Product of the zeros = -12
$=\frac{-12}{1}=\frac{\text{Constant term}}{\text{Coefficient of }\text{x}^2}$
Sum of the zeros $=(\alpha+\beta)$
$=2+(-6) =- 4$
Product of the zeros $=\alpha\beta$
$=2\times(-6) =- 12$
$\therefore$ Required polynomial $=\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$=\text{x}^2-(-4)\text{x}-12$
$=\text{x}^2+\text{4x}-12$
Sum of the zeros = -4
$=\frac{-4}{1}=\frac{-(\text{Coefficient of x})}{(\text{Coefficient of }\text{x}^2)}$
Product of the zeros = -12
$=\frac{-12}{1}=\frac{\text{Constant term}}{\text{Coefficient of }\text{x}^2}$
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