Question

If α and β are the roots of the quadratic equation x² + px + 12 = 0 with the condition α – β = 1, then the value of ‘p’ is 

A) 7 or -7 

B) 1 

C) -7 

D) 7

Answer 1

Correct option is (A) 7 or -7

Given quadratic equation is

\(x^2+ px + 12 = 0\)

\(\therefore\) Sum of roots = -p

\(\Rightarrow\) \(\alpha+\beta\) = -p    _______________(1)

Product of roots = 12

\(\Rightarrow\) \(\alpha\beta\) = 12       _______________(2)

Given that \(\alpha-\beta\) = 1    _______________(3)

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

\(=1^2+4\times12\)        (From (2) & (3))

\(=1+48=49\)

\(\Rightarrow\) \(\alpha+\beta\) \(=\pm7\)

\(\Rightarrow\) -p \(=\pm7\)           (From (1))

\(\Rightarrow\) p \(=\mp7\)

\(\Rightarrow p=-7\;or\;p=7\)

Hence, value of p is -7 or 7.

Answer 2

Correct option is A) 7 or -7

Answer 3

will be edited after 2-3 hr