Question

Find a Quadratic polyinomial each with the given number as the sum and product of its zeroes respectively 1/4 and -1

Answer 1

Answer:

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Answer 2

$\sf{\large{\underline{\underline{EXPLANATION:}}}}$

Let the zeroes 1/4 and -1 be alpha and beta respectively.

Therefore,

$\alpha + \beta = \frac{1}{4} + ( - 1) = \frac{ - 3}{4}$

and

$\alpha \beta = \frac{1}{4} ( - 1) = \frac{ - 1}{4}$

$\textbf{\underline{Using formula,,}}</p><p>$

Quadratic polynomial,,

$a {x}^{2} + bx + c = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = {x}^{2} - \frac{ ( - 3x)}{4} + \frac{( - 1)}{4} \\ = {x}^{2} + \frac{3x}{4} - \frac{1}{4}$

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