Question

if x = 2/3and x = - 3are roots of a x square + 7 x + b =0 find a and b​

Answer 1

Substituting x = 2/3

$a {( \frac{2}{3} )}^{2} + 7( \frac{2}{3} ) + b = 0 \\ \frac{4a}{9} + \frac{14}{3} + b = 0 \\ 4a +4 2 + 3b = 0 \\ 4a + 3b = - 42 \: \: \: \: = > > (i)$

Substituting x = -3

$a( { - 3)}^{2} + 7( - 3) + b = 0 \\ 9a - 21 + b = 0 \\ 9a + b = 21 \\ 27a + 3b = 63 \: \: = > > (ii)$

Subtracting (ii) from (i) we get,

$4a - 27a = - 42 - 63 \\ 23a = 105 \\ a = \frac{23}{105}$

Therefore,

$b = 21 - 9( \frac{23}{105} ) \\ b = 21 - \frac{69}{35} \\ b = \frac{735 - 69}{35} = \frac{666}{35}$