If x2 + 4ax + 3 = 0 and 2x2 + 3ax – 9 = 0 have a common root, then t

1.	If x2 + 4ax + 3 = 0 and 2x2 + 3ax – 9 = 0 have a common root, then the value of ‘a’ is ……………A) 1 B) ± 3 C) ± 1D) -3
Answer» Correct option is (C) ± 1 Let \(\alpha\) be common root of equations \(x^2+4ax+3=0\) and \(2x^2+3ax-9=0\) \(\therefore\) \(\alpha^2+4a\alpha+3=0\) _______________(1) \(2\alpha^2+3a\alpha-9=0\) _______________(2) Multiply equation (1) by 2, we get \(2\alpha^2+8a\alpha+6=0\) _______________(3) Subtract equation (2) from (3), we get \((2\alpha^2+8a\alpha+6)-(2\alpha^2+3a\alpha-9)\) \(=0-0=0\) \(\Rightarrow5a\alpha+15=0\) \(\Rightarrow a\alpha=\frac{-15}5=-3\) _______________(4) Put \(a\alpha=-3\) into equation (1), we get \(\alpha^2-12+3=0\) \(\Rightarrow\) \(\alpha^2-9=0\) \(\Rightarrow\) \(\alpha^2=9\) \(\Rightarrow\) \(\alpha=\pm3\) Then from (4), we get \(a=\frac{-3}\alpha=\frac{-3}{\pm3}=\mp1\) \(\therefore\) a = \(\pm\,\,1\) Correct option is C) ± 1

If x2 + 4ax + 3 = 0 and 2x2 + 3ax – 9 = 0 have a common root, then the value of ‘a’ is ……………A) 1 B) ± 3 C) ± 1D) -3

Answer»

Correct option is (C) ± 1

Let \(\alpha\) be common root of equations

\(x^2+4ax+3=0\) and \(2x^2+3ax-9=0\)

\(\therefore\) \(\alpha^2+4a\alpha+3=0\) _______________(1)

\(2\alpha^2+3a\alpha-9=0\) _______________(2)

Multiply equation (1) by 2, we get

\(2\alpha^2+8a\alpha+6=0\) _______________(3)

Subtract equation (2) from (3), we get

\((2\alpha^2+8a\alpha+6)-(2\alpha^2+3a\alpha-9)\) \(=0-0=0\)

\(\Rightarrow5a\alpha+15=0\)

\(\Rightarrow a\alpha=\frac{-15}5=-3\) _______________(4)

Put \(a\alpha=-3\) into equation (1), we get

\(\alpha^2-12+3=0\)

\(\Rightarrow\) \(\alpha^2-9=0\)

\(\Rightarrow\) \(\alpha^2=9\)

\(\Rightarrow\) \(\alpha=\pm3\)

Then from (4), we get

\(a=\frac{-3}\alpha=\frac{-3}{\pm3}=\mp1\)

\(\therefore\) a = \(\pm\,\,1\)

Correct option is C) ± 1