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Statement 1 : The equations \[2{{x}^{2}}+kx-5=0\] and \[{{x}^{2}}-3x-4=0\]have one root in common i.e., \[k=-3\,or\,k=-\frac{27}{4}.\]

Statement 2 : 1 The required condition for one root to be common of two quadratic equations\[{{a}_{1}}{{x}^{2}}+{{b}_{1}}x+{{c}_{1}}=0\] and \[{{a}_{2}}{{x}^{2}}+{{b}_{2}}x+{{c}_{2}}=0\]is \[({{a}_{1}}{{b}_{2}}-{{b}_{1}}{{a}_{2}})\,({{b}_{1}}{{c}_{2}}-{{b}_{2}}{{c}_{1}})={{({{c}_{1}}{{a}_{2}}-{{c}_{2}}{{a}_{1}})}^{2}}.\]

 

A)  Both Statement 1 and Statement 2 are true and Statement 2 is correct explanation of Statement 1.

B)  Both Statement 1 and Statement 2 are true but Statement 2 is not correct explanation of Statement 1.

C)  Statement 1 is true, Statement 2 is false.

D)  Statement 1 is false, Statement 2 is true.