Question

find the quardict polynomial if the zero of it are 2 and-⅓ respectively​

Answer 1

FINAL ANSWER:-

QUADRATIC POLYNOMIAL ⇔ $3x^{2}-5x-2$

GIVEN:-

zeroes of it are 2 and $\frac{-1}{3}$

∴ zeroes of polynomial ⇒  [$\alpha =2 \: and\:\beta =\frac{-1}{3}$]

TO FIND:-

the quadratic polynomial

SOLUTION:-

let take the α and β variable as $'x'$

$So,\\x=2\:\:\:;\:\:\:x=\frac{-1}{3} \\x-2=0\:\:\:;\:\:\:3x=-1\\x-2=0\:\:\:;\:\:\:3x+1=0$

Now,

as we get x-2 and  now multiply them to get quadratic polynomial

$(x-2)(3x+1)=0\\x(3x+1)-2(3x+1)=0\\3x^{2}+x-6x-2=0\\3x^{2}-5x-2=0$

==================================================================

to cross check our answer:-

(using factorisation method)

$3x^{2}-5x-2=0\\3x^{2}+x-6x-2=0\\x(3x+1)-2(3x+1)=0\\(x-2)(3x+1)=0$

$x-2=0\:\:\:\:\:and\:\:\:\:\:3x+1=0\\x=2\:\:\:\:\:and\:\:\:\:\:x=\frac{-1}{3}$

hence successfully checked