The difference of the roots of x2 – 7x – 9 = 0 is A) \(\sqrt{85}

1.	The difference of the roots of x2 – 7x – 9 = 0 is A) \(\sqrt{85}\)B) 7 C) -9 D) 8
Answer» Correct option is (A) \(\sqrt{85}\) Let \(\alpha\;and\;\beta\) are roots of \(x^2-7x-9=0\) \(\therefore\) Sum of roots \(=\frac{-(-7)}1=7\) \(\Rightarrow\) \(\alpha+\beta=7\) _____________(1) And product of roots \(=\frac{-9}1=-9\) \(\Rightarrow\) \(\alpha\beta=-9\) _____________(2) Now, \((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta\) \(=7^2-4\times-9\) = 49+36 = 85 \(\therefore\) \(\alpha-\beta=\sqrt{85}\) Hence, difference of roots of given equation is \(\sqrt{85}.\) Correct option is A)\(\sqrt{85}\)

The difference of the roots of x2 – 7x – 9 = 0 is A) \(\sqrt{85}\)B) 7 C) -9 D) 8

Answer»

Correct option is (A) \(\sqrt{85}\)

Let \(\alpha\;and\;\beta\) are roots of \(x^2-7x-9=0\)

\(\therefore\) Sum of roots \(=\frac{-(-7)}1=7\)

\(\Rightarrow\) \(\alpha+\beta=7\) _____________(1)

And product of roots \(=\frac{-9}1=-9\)

\(\Rightarrow\) \(\alpha\beta=-9\) _____________(2)

Now, \((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta\)

\(=7^2-4\times-9\)

= 49+36 = 85

\(\therefore\) \(\alpha-\beta=\sqrt{85}\)

Hence, difference of roots of given equation is \(\sqrt{85}.\)

Correct option is A)\(\sqrt{85}\)