Question

find a quadratic equation whose zeroes are -1/4 and 1/4​

Answer 1

Answer:

(x+1/4) (x-1/4) is the quadratic equation of the given zeroes

Answer 2

$\underline{\boxed{\bold{Question}}}$  

↠ Find a quadratic equation whose zeroes are -1/4 and 1/4​

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$\underline{\boxed{\bold{Important\;Information}}}$  

↠ Sum of roots = (-b)/a

↠ Product of roots = c/a

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$\underline{\boxed{\bold{Given}}}$

↠ First root = α = (-1/4)

↠ Second root = β = (1/4)

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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Every quadratic equation can be expressed in form given below.

$\boxed{\bold{\red{\leadsto x^{2} -(\alpha +\beta )x + \alpha \beta }}}$

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So let's find value of α + β

$:\implies \alpha + \beta = Sum \ of \ roots$

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

$\boxed{\blue {:\implies \alpha + \beta = 0}}$

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Now let's find value of αβ

$:\implies \alpha \beta = Product \ of \ roots$

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

$\boxed{\blue {:\implies \alpha \beta = ( \frac{-1}{16} )}}$

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Now let's substitute values in the given equation.

$:\implies x^{2} -(\alpha +\beta )x + \alpha \beta = 0$

$:\implies x^{2} -(0)x + (\frac{-1}{16} ) = 0$

$\red {:\implies x^{2} - \frac{1}{16} = 0}$

$\blue {:\implies 16x^{2} - 1 = 0}$

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$\boxed{\boxed{\bold{\therefore Required \; Equation = 16x^{2} - 1 = 0}}}$

$\boxed{\boxed{\bold{\therefore Required \; Equation = x^{2} - \frac{1}{16} = 0}}}$

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Hope this helps u.../

【Brainly Advisor】