Question

Write the quadratic equation whose zeroes are -2 and -1/3..
please help urgently​

Answer 1

Your Answer:

Given:-

• Two zeroes are -2 and -1/3

To Find:-

• The Quadratic Equation

Solution:-

Let

$\tt \alpha = -2 \\\\ \tt and\\\\ \tt \beta = \dfrac{-1}{3}$

where alpha and beta are the zeroes

So, to find the Quadratic Equation we must form a equation in this form

$\tt k[x^2-(Sum\:\:of\:\:Zeroes)x +(Product\:\:of\:\:Zeroes)] \\\\ \tt \Rightarrow k[x^2-(\alpha+\beta)x+(\alpha\beta)]\\\\ \tt \Rightarrow k[x^2- (-2-\dfrac{1}{3})x+[(-2)(\dfrac{-1}{3})]] \\\\ \tt \Rightarrow k[x^2-(\dfrac{-7}{3})x+(\dfrac{2}{3})] \\\\ \tt \Rightarrow k[x^2+\dfrac{7}{3}x+\dfrac{2}{3}] \\\\ \tt let \:\:\:k=3 (because \:\:LCM\:\:of\:\:denominator\:\:is \:\:3)\\\\ \tt \Rightarrow 3x^2+7x+2$

So, the Quadratic Equation is 3x^2+7x+2