Question

If 𝛼 and 𝛽 be the zeroes of the polynomial ${\displaystyle 2x^2-7x+k}$ write the value of (𝛼 + 𝛽+ 𝛼 𝛽.                                     

Answer 1

By using the relationship between the zeroes of he quadratic polynomial.
We have  

Sum of zeroes=${\displaystyle \frac{-\left(\text{Coefficient of x}\right)}{\text{Coefficient of}{x}^2}}$ and Product of zeroes =${\displaystyle \frac{\text{Constant term}}{\text{Coefficient of}{x}^2}}$ 

${\displaystyle \therefore \propto +\beta =\frac{-7}{2}\text{and}\propto \beta =\frac{5}{2}}$ 

Now, 𝛼 + 𝛽 + 𝛼𝛽 =${\displaystyle \frac{-7}{2}+\frac{5}{2}=-1}$