Question

Find the values of and b for which x=3/4and x=-2 are the roots of the equation ax²+bx-6=0

Answer 1

Step-by-step explanation:

a=4, b=5 is correct and for this

Answer 2

Answer:

a =4 , b =5

Explanation :

p ( x) = ax^2 + bx - 6 =0

p (3/4) = a × (3/4)^2 + b × 3/4 - 6 = 0

= 9a/16 + 3b/4 - 6 =0

= 9a +12b - 96 =0 (taking LCM )

= 9a+12b =96

= 3 (3a+4b)=96

=3a +4b = 96 /3

= 3a + 4b = 32 _____ (i)

p ( -2) = ax^2 + bx - 6 =0

= a × (- 2) ^2 + b × ( -2) - 6 =0

= 4a^2 -2b - 6 =0

= 4a - 2b = 6

= 2( 2a - b) =6

= 2a - b = 6/2 =3

= 2a - b = 3

Multiplying both sides by 4

8a - 4b = 12 ___(ii)

Adding equation ( i) and (ii) ,

3a + 8a + 4b - 4b = 32 +12

= 11a = 44

a = 44 /11 = 4

Therefore , 2a -b =3

= 2× 4 - b = 3

8- b = 3

b = 5