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Find the quadratic polynomial whose sum and product of the zeros are \( \frac{21}{8} \) and \( \frac{5}{16} \) respectively. |
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Answer» Let the required zeroes be \(α\) , \(β\) \(α + β = \frac{21}{8} = \frac{42}{16} = \frac{-b}{a}\) \(... (1)\) \(αβ = \frac{5}{16} = \frac{c}{a}\) \(... (2)\) From (1) and (2), \(b = -42\) , \(a = 16\) , \(c = 5\) Required polynomial is \(16x^2 - 42x + 5 \) Let α & ß are zeros of quadratic polynomial. α + ß = 21/8 ⇒ -b/a = 21/8---(1) αß = 5/16 ⇒ c/a = 5/16--(2) From (1), -b/a = 21/8 = 42/16 ∴ a = 16, b = -42, c = 5 Required quadratic polynomial is p(x) = ax2 + bx + c = 16x2 - 42x + 5 |
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