Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and coefficients of xsquare-9​

Answer 1

Step-by-step explanation:

x^2-9=0

x^2=9

x=root 9

x=3, -3

verifying relationships

a+b=3+(-3)

a+b=0

a+b=-b/a

a+b=0/1=)0

a×b=3×(-3)=)-9

a×b=c/a=)-9/1=-9

hence verified

Answer 2

✯✯ QUESTION ✯✯

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and coefficients of x²-9..

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✰✰ ANSWER ✰✰

$\longrightarrow{{x}^{2}-9}$

Using Identity : -

$\longrightarrow{{a}^{2}-{b}^{2}=(a+b)(a-b)}$

$\longrightarrow{({x}^{2}+(-9)({x}^{2}-(-9)}$

$\longrightarrow{({x}^{2}-9)({x}^{2}+9)}$

Now ,

$\longrightarrow{{x}^{2}-9=0}$

$\longrightarrow{{x}^{2}=\sqrt{9}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{3}}}$

$\longrightarrow{{x}^{2}+9=0}$

$\longrightarrow{{x}^{2}=\sqrt[-]{9}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\orange{x}\green{=}\blue{-3}}}$

So , 3 and -3 are the zeroes of polynomials x²-9..

Now ,

➥Sum of Zeroes : -

$\longrightarrow{\alpha+\beta=\dfrac{-b}{a}}$

$\longrightarrow{3+(-3)=\dfrac{-(-0)}{1}}$

$\longrightarrow{0=0}$

$\red\longmapsto\:\large\underline{\boxed{\bf\pink{L.H.S}\blue{=}\green{R.H.S}}}$

➥Product of Zeroes : -

$\longrightarrow{\alpha\beta=\dfrac{c}{a}}$

$\longrightarrow{3\times{-3}=\dfrac{-9}{1}}$

$\longrightarrow{-9=-9}$

$\pink\longmapsto\:\large\underline{\boxed{\bf\purple{L.H.S}\green{=}\red{R.H.S}}}$