Question

If x2+ax+5=0 and x2-3x+2=0 has one common root then ‘a’ is

Answer 1

Answer:

$a = - 6 \: \: or \: \: a = - \frac{9}{2}$

Step-by-step explanation:

${x}^{2} - 3x + 2 = 0 \\ \\ {x}^{2} - x - 2x + 2 = 0 \\ \\ x(x - 1) - 2(x - 1) = 0 \\ \\ (x - 1)(x - 2) = 0 \\ \\x = 1 \\ x = 2 \\ \\ {x}^{2} + ax + 5 = 0 \\ \\ if \: \: 1 \: \: is \: common \: root \\ {1}^{2} + a(1) + 5 = 0 \\ \\ a = - 6 \\ \\ if \: \: 2 \: \: is \: common \: root \\ {2}^{2} + a(2) + 5 = 0 \\ \\ 2a + 9 = 0\\ \\ a = - \frac{9}{2}$

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