please solve it .

Asked by shahbaaz.rocking | 9th Aug, 2020, 06:44: PM

Expert Answer:

2/3 and -1/2 are solutions of quadratic equation 6x2 + ax - b = 0, find the values of a and b.
 
Solution:
2/3 and -1/2 are solutions of quadratic equation 6x2 + ax - b = 0 ... (i)
This means they satisfies (i)
rightwards double arrow 6 open parentheses 2 over 3 close parentheses squared plus straight a open parentheses 2 over 3 close parentheses minus straight b equals 0 space space and space 6 open parentheses negative 1 half close parentheses squared plus straight a open parentheses negative 1 half close parentheses minus straight b equals 0
rightwards double arrow 8 over 3 plus 2 over 3 straight a minus straight b equals 0 space space and space 3 over 2 minus straight a over 2 minus straight b equals 0
rightwards double arrow 8 plus 2 straight a minus 3 straight b equals 0 space... space left parenthesis straight i right parenthesis space and space 3 minus straight a minus 2 straight b equals 0 space... space left parenthesis ii right parenthesis
Multiplying space left parenthesis ii right parenthesis space by space 2 comma space we space get space
6 minus 2 straight a minus 4 straight b equals 0 space... space left parenthesis iii right parenthesis
Adding space left parenthesis straight i right parenthesis space and space left parenthesis iii right parenthesis comma space we space get
14 minus 7 straight b equals 0 rightwards double arrow straight b equals 2
rightwards double arrow straight a equals negative 1

Answered by Renu Varma | 12th Aug, 2020, 01:22: PM