Question

find the quadratic polynomial for the zeores 2 and -5​

Answer 1

Given : Zeroes of a quadratic polynomial are 2 and -5 respectively.

To Find : The quadratic polynomial.

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As we know that :

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$\star \: \underline{\boxed{\mathfrak\purple{quadratic \: polynomial = {x }^{2} \: - (sum \: of \: zeroes)x \: + product \: of \: zeroes}}}$

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Finding sum of zeroes :

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$\sf\implies \: α + β \: = 2 \: + \: ( - 5) \\ \\ \\ \sf\implies \: α + β \: = 2 \: - \: 5 \\ \\ \\ \sf\implies \: \underline{\boxed{\sf\purple{α + β \: = \bold{ - 3}}}} \: \bigstar$

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Finding product of zeroes :

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$\sf\implies \: α \times β \: = 2 \: \times \: ( - 5) \\ \\ \\ \sf\implies \: \underline{\boxed{\sf\purple{α \times β \: = \bold{ - 10}}}} \: \bigstar$

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✪ Now, put the values in the formula and solve.

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$\sf:\implies \: quadratic \: polynomial \: = {x}^{2} - (α + β)x + (α \times β) \\ \\ \\ \sf:\implies \: quadratic \: polynomial \: = {x}^{2} - ( - 3) x \: + \: (- 10) \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{quadratic \: polynomial \: = {x}^{2} + 3x - 10}}} \:\bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: quadratic \: polynomial \: is \: \bold{ {x}^{2} + 3x - 10}. }}$

Answer 2

Answer:

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