If α, β are the roots of x2 – 10x + 9 = 0, then | α – β| = A)

1.	If α, β are the roots of x2 – 10x + 9 = 0, then \| α – β\| = A) 9 B) 8 C) -10D) 10
Answer» Correct option is (B) 8 Given that \(\alpha,\beta\) are roots of \(x^2-10x+9=0\) \(\therefore\) Sum of roots \(=\frac{-(-10)}1=10\) \(\Rightarrow\) \(\alpha+\beta=10\) ______________(1) And product of roots \(=\frac91=9\) \(\Rightarrow\) \(\alpha\beta=9\) ______________(2) Now, \((\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta\) \(=10^2-4\times9\) = 100 - 36 = 64 \(=8^2\) \(\Rightarrow\) \(\|\alpha-\beta\|=8\) Correct option is B) 8

If α, β are the roots of x2 – 10x + 9 = 0, then | α – β| = A) 9 B) 8 C) -10D) 10

Answer»

Correct option is (B) 8

Given that \(\alpha,\beta\) are roots of \(x^2-10x+9=0\)

\(\therefore\) Sum of roots \(=\frac{-(-10)}1=10\)

\(\Rightarrow\) \(\alpha+\beta=10\) ______________(1)

And product of roots \(=\frac91=9\)

\(\Rightarrow\) \(\alpha\beta=9\) ______________(2)

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

\(=10^2-4\times9\)

= 100 - 36

= 64 \(=8^2\)

\(\Rightarrow\) \(|\alpha-\beta|=8\)

Correct option is B) 8