ax² - 13x +b = 0; x=2/3 and 3/2 then find a and b
a x2-13 x + b =0
p(2/3) = a(2/3)2- 13 (2/3) + b =0
= 4 a/9 - 26/3 +b =0
( taking LCM as 9 )
= 4 a - 78 +9 b =0 ----- 1
p ( 3/2) = a [ 3/2]2 - 13 [ 3/2 ] +b =0
after solving the equation ----- 9 a - 78 +4 b = 0 ------- 2
adding 1 and 2
13 a +13 b= 156 -------3
subtracting 1 and 2
-5 a+5 b=0
a=b -------4
putting 4 in 3
13 a + 13 b = 156
13 a + 13 a = 156
26 a = 156
a = 6
therefore : b=6
p(2/3) = a(2/3)2- 13 (2/3) + b =0
= 4 a/9 - 26/3 +b =0
( taking LCM as 9 )
= 4 a - 78 +9 b =0 ----- 1
p ( 3/2) = a [ 3/2]2 - 13 [ 3/2 ] +b =0
after solving the equation ----- 9 a - 78 +4 b = 0 ------- 2
adding 1 and 2
13 a +13 b= 156 -------3
subtracting 1 and 2
-5 a+5 b=0
a=b -------4
putting 4 in 3
13 a + 13 b = 156
13 a + 13 a = 156
26 a = 156
a = 6
therefore : b=6