Question

if x=1 is the common root of the equations a x squared +a x+3=0 and x squared+x+b=0 then the value of ab is

Answer 1

${ax}^{2} + ax + 3 = 0 \\ x = 1 \\ a {(1)}^{2} + a(1) + 3 = 0 \\ a + a = - 3 \\ 2a = - 3 \\ a = - 1.5$
${x}^{2} + x + b = 0 \\ x = 1 \\ {(1)}^{2} + 1 + b = 0 \\ 2 + b = 0 \\ b = - 2$
$ab = ( - 1.5) \times ( - 2) \\ ab = 3$
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