Question

if x=1 is a common root of quadratic equation ax²+ax+b=0 and x²+x+b=0 then ab= ​

Answer 1

Answer:

ab = -2. I hope it may help.you

Answer 2

$Given \: x = 1 \: is \: a \: common$

$root \: of \: Quadratic \: equation$

$ax^{2}+ax+b=0 \:and$

$x^{2}+x+b = 0$

$i)Put \:x = 1 \: in \: ax^{2} +ax+b=0 ,we \:get$

$a \times 1^{2} + a\times 1 + b = 0$

$\implies a + a + b = 0$

$\implies 2a = - b$

$\implies a = \frac{-b}{2} \: --(1)$

$ii) Put \:x = 1 \:in \: x^{2}+x+b =0 , we \:get$

$1^{2} + 1 + b= 0$

$\implies 1+1 + b = 0$

$\implies b = -2 \:--(2)$

/* Put b = -2 in equation (1), we get */

$a = \frac{-(-2)}{2}$

$\implies a = 1$

$Now, \red{ Value \: of \: ab }$

$= 1 \times (-2)$

$= -2$

Therefore.,

$\red{ Value \:of \: ab } \green { = -2}$

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