Question

1From the quadratic equation form the roots given below.
1upon 2 , -1upon 2​

Answer 1

Answer:

$4 {x}^{2} - 1$

Step-by-step explanation:

$let \: \alpha = \frac{1}{2} \\ let \: \beta = \frac{ - 1}{2}$

Using the formula:

$f(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \times \beta$

By substituting appropriate values, we get

$f(x) = {x}^{2} - ( \frac{1}{2} + \frac{( - 1)}{2} )x + ( \frac{1}{2} \times \frac{( - 1)}{2} ) \\ f(x) = {x}^{2} - (0)x - \frac{1}{4} \\ f(x) = 4 {x}^{2} - 1$

Hope it helped you!!