Question

find a quadratic equations whose zeroes are 1 by 4 and -1​

Answer 1

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༒ Given :-

For a Quadratic Equation

1st Zero = α = 1/4

2nd Zero = β = -1

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༒ To Find :-

The Quadratic Equation

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༒ Key Point :-

If sum and product of zeros of any quadratic equation are s and p respectively,

Then,

The quadratic equation is given by :-

$\bf  {x}^{2}  - s \: x + p=0$

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༒ Solution :-

Sum of Zeros = α + β

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

Product of Zeros = αβ

$= \sf \frac{1}{4} ( - 1) \\ \\ \sf = \frac{ - 1}{4}$

So,

Sum = s = -3/4

and

Product = p = -1/4

So,

Required Equation should be

$\sf {x}^{2} + \frac{3}{4} x - \frac{1}{4} = 0 \\ \\ \large\purple{ \underline {\boxed{\bf 4 {x}^{2} + 3x - 1 = 0}}}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

$\blue{ \fcolorbox{purpLe}{black}{ \boxed{ \orange{ \star}{ \bold{\: Answer }\orange{\star}}}}}$

Sum of Zeros = α + β

$</p><p>\begin{gathered} \sf = \frac{1}{4} + ( - 1) \\ \\ \sf = \frac{1}{4} - 1 \\ \\ = \sf \frac{ - 3}{4} \end{gathered}$

Product of Zeros = αβ

$\begin{gathered} = \sf \frac{1}{4} ( - 1) \\ \\ \sf = \frac{ - 1}{4} \end{gathered}$

So,

Sum = s = -3/4

and

Product = p = -1/4

So,

Required Equation should be

$\begin{gathered} \sf {x}^{2} + \frac{3}{4} x - \frac{1}{4} = 0 \\ \\\large\purple{ \underline {\boxed{\bf 4 {x}^{2} + 3x - 1 = 0}}}\end{gathered} </p><p>$