Question

if the sum and product of zeroes are 3/4 and -1 then find quadratic equation​

Answer 1

$\bf{\underline{\underline{Question:-}}}$

• if the sum and product of zeroes are 3/4 and -1 then find quadratic equation.

$\bf{\underline{\underline{Given:-}}}$

• Sum of zeroes 3/4
• Product of zeroes -1

$\bf{\underline{\underline{We\: Know:-}}}$

• Product of zeroes $\sf \alpha × \beta$

$\sf Product\:of\:zeroes = \frac{3}{4}×-1$

$\sf Product\:of\:zeroes = \frac{-3}{4}$

• Sum of zeroes $\sf \alpha+\beta$

$\sf Sum\: of \:zeroes = \frac{3}{4}+-1$

$\sf Sum \:of \:zeroes = \frac{3-4}{4} = \frac{-1}{4}$

$\bf{\underline{\underline{Solution:-}}}$

A Quadratic equation = $\sf x^2 + (\alpha+\beta)x+(\alpha×\beta)=0$

OR

$\sf † \:x^2 +(sum\:of\:zeroes )x+(Product\:of\:Zeroes)=0$

$\sf → x^2 + \frac{-3}{4}x+ \frac{-1}{4}=0$

$\sf → x^2 -\dfrac{3}{4}x-\dfrac{1}{4}=0$

$\sf → x^2-\dfrac{3}{4}x\: -\dfrac{1}{4}=0$

$\sf → 4x^2-3x-\dfrac{1}{4}=0$

$\sf → 4x^2-12x-1=0$

$\bf{\underline{\underline{Hence:-}}}$

• the required polynomial is $\sf 4x^2-12x-1=0$

Answer 2

Answer:

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