if2/3 and -1/2 are solutions of quadratic 6x²+ax-b=0 find values of a and b
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Given :-
Solution of Quadratic equation are -
→ 2/3 and -1/2
Quadratic equation = 6x² + ax -b = 0
Solution :-
Putting x = 2/3
→ 6(2/3)² + a(2/3) -b = 0
→ 6(4/9) + 2a/3 - b = 0
→ 4×2/3 + 2a/3 - b = 0
→ 8/3 + 2a /3 = b
→ 8 + 2a = 3b
→ (8+2a)/3 = b
Putting x = -1/2
→ 6(-1/2)² + a(-1/2) -b = 0
→ 6/4 - a/2 = b
→ 3/2 - a/2 = b
→ 3 - a = 2b
Here putting the value of b
→ 3 - a = 2[(8+2a)/3 ]
→ (3-a ) 3 = 16 +4a
→ 9 - 3a = 16+ 4a
→ 9-16 = 7a
→ -7 = 7a
a = -1 .
Putting value of a in any equation .
→ 8 + 2(-1) /3 = b
→ 8-2 /3 = b
→ 6/3 = b
→ 2 = b .
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