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If x-(2)/(3) and x+3 are factors of the ...

If `x-(2)/(3)` and `x+3` are factors of the quadratic polynomial `ax^(2)+7x+b`, then find the values of `a` and `b`.

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To solve the problem, we need to find the values of \( a \) and \( b \) in the quadratic polynomial \( ax^2 + 7x + b \) given that \( x - \frac{2}{3} \) and \( x + 3 \) are factors of this polynomial. ### Step-by-Step Solution: 1. **Identify the Roots:** The factors of the polynomial imply that the roots of the polynomial are: \[ x = \frac{2}{3} \quad \text{and} \quad x = -3 ...
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