Question

Find the quadratic polynomial whose zeroes are given as -3, 5. Choose the correct option:
A. \[{{x}^{2}}-3x-15\]
B. \[{{x}^{2}}-2x-7\]
C. \[{{x}^{2}}-2x-15\]
D. \[{{x}^{2}}-2x+15\]

Answer 1

Hint: The quadratic equation with the roots \[\alpha ,\beta \] is given by \[(x-\alpha )(x-\beta )=0\].

Complete step by step answer:
In the question, we have to find the quadratic polynomial whose zeroes are -3, 5.
Now we know that if we have roots \[\alpha ,\beta \], then the quadratic equation will be \[(x-\alpha )(x-\beta )=0\] and the quadratic polynomial will be \[(x-\alpha )(x-\beta )\].
Now, here we are given with the roots \[\alpha =-3,\,\,\beta =5\]. So, the quadratic equation will be, as follows:
\[\begin{align}
  & \Rightarrow (x-\alpha )(x-\beta )=0 \\
 & \Rightarrow (x+3)(x-5)=0 \\
 & \Rightarrow x\times x-5x+3x-3\times \;5=0 \\
 & \Rightarrow {{x}^{2}}-2x-15=0 \\
\end{align}\]
So now the required quadratic polynomial will be \[{{x}^{2}}-2x-15\].
Hence the correct answer is option (C) \[{{x}^{2}}-2x-15\].

Note: There is a difference between the equation and the polynomial. The equation is \[(x-\alpha )(x-\beta )=0\] , but the polynomial is just \[(x-\alpha )(x-\beta )\].