for what values of a and b,x=3/4 and x=-2 are the solutions of the equation ax२+bx-6=0
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Given Quadratic equation is ax^2 + bx - 6 = 0.
Given roots of the equation are x = -3/4 and x = -2.
(i) when x = -3/4 then the equation will be
a(3/4)^2 + b(3/4) - 6 = 0
9a/16 + 3b/4 - 6 = 0
9a + 12b - 96 = 0
3a + 4b - 32 = 0
a = 32 - 4b/3----------- (1)
(ii) when x = -2 then the equation will be
a(-2)^2 + b(-2) - 6 = 0
4a - 2b - 6 = 0
2a - b - 3 = 0
2a - b = 3 ---------- (2)
Substitute (1) in (2), we get
2(32 - 4b/3) - b = 3
2(32 - 4b) - 3b = 9
64 - 8b - 3b = 9
64 - 11b = 9
-11b = -55
b = 5
Substitute b = 5 in (2), we get
2a - b = 3
2a - 5 = 3
2a = 8
a = 8/2
a = 4.
Therefore the value is a = 4.
the value of b = 5.
Hope this helps!
Given roots of the equation are x = -3/4 and x = -2.
(i) when x = -3/4 then the equation will be
a(3/4)^2 + b(3/4) - 6 = 0
9a/16 + 3b/4 - 6 = 0
9a + 12b - 96 = 0
3a + 4b - 32 = 0
a = 32 - 4b/3----------- (1)
(ii) when x = -2 then the equation will be
a(-2)^2 + b(-2) - 6 = 0
4a - 2b - 6 = 0
2a - b - 3 = 0
2a - b = 3 ---------- (2)
Substitute (1) in (2), we get
2(32 - 4b/3) - b = 3
2(32 - 4b) - 3b = 9
64 - 8b - 3b = 9
64 - 11b = 9
-11b = -55
b = 5
Substitute b = 5 in (2), we get
2a - b = 3
2a - 5 = 3
2a = 8
a = 8/2
a = 4.
Therefore the value is a = 4.
the value of b = 5.
Hope this helps!
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