Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeros and the coefficient x²+x-2

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Solution :

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

The quadratic polynomial x² + x - 2.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The zeroes and verify the relationship between the zeroes and the coefficient.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We have p(x) = x² + x - 2

Zero of the polynomial p(x) = 0

So;

$\longrightarrow\sf{x^{2} +x-2=0}\\\\\longrightarrow\sf{x^{2} +2x-x-2=0}\\\\\longrightarrow\sf{x(x+2)-1(x+2)=0}\\\\\longrightarrow\sf{(x+2)(x-1)=0}\\\\\longrightarrow\sf{x+2=0\:\:\:Or\:\:\:x-1=0}\\\\\longrightarrow\sf{\pink{x=-2\:\:\:Or\:\:\:x=1}}$

∴ The α = -2 and β = 1 are the zeroes of the polynomial.  

As the given quadratic polynomial as we compared with ax² + bx + c

• a = 1
• b = 1
• c = -2

Now;

$\star\:{\green{\underline{\boldsymbol{Sum\:of\:the\:zeroes\::}}}}}$

$\longrightarrow\sf{\alpha +\beta =\dfrac{-b}{a} =\dfrac{Coefficient\:of\:x }{Coefficient\:of\:x^{2} }} \\\\\\\longrightarrow\sf{-2+1=\dfrac{-1}{1} }\\\\\\\longrightarrow\sf{\pink{-1=-1}}$

$\star\:{\green{\underline{\boldsymbol{Product\:of\:the\:zeroes\::}}}}}$

$\longrightarrow\sf{\alpha \times \beta =\dfrac{c}{a} =\dfrac{Constant\:term }{Coefficient\:of\:x^{2} }} \\\\\\\longrightarrow\sf{-2\times 1=\dfrac{-2}{1} }\\\\\\\longrightarrow\sf{\pink{-2=-2}}$

Thus;

Relationship between zeroes and coefficient is verified .