Question

if x = 2/3 and x = -3 are the roots of the equation $ax^{2} + 7x + b = 0$,
find the values of a and b

Answer 1

★Given:-

➠ Roots of the equation are 2/3 and-3.

➠ Equation ax² + 7x + b = 0

★To find:-

➠ Value of a and b.

★Solution:-

➠ Putting the value of x = 2/3 in the given equation.

➠ a(2/3)² + 7(2/3) + b = 0

➠ a4/9 + 14/3 + b = 0

➠ 4a + 9b = 14/3 × 9

➠ 4a + 9b = 42.........(i)

➠Now, putting the value of x = -3 in the given equation.

➠ a(-3)² + 7(-3) + b = 0

➠ 9a - 21 + b = 0

➠ 9a + b = 21.........(ii)

On multiplying 9 with equation (ii) , we get

4a + 9b = 42

81a + 9b = 189

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-77a + 0 = -147..........(iii)

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➠ Solving equation (iii)

➠ -77a = -147

➠ a = 147/77

➠ Putting the value of a in equation (ii)

➠ 9 × 147/77 + b = 21

➠ 1323/77 + b = 21

➠ b = 1617/1323