Question

verify the relation between zeroes and coefficients of the quadratic polynomial x square minus 4

Answer 1

Heya here ....

Solution -----------------------------------

we have
f (x) = ( x^2 - 4 )
=> {x^2 - (√4)^2}
=> (x + √4 ) ( x - √4 ).

f (x) =0
=> (x + √4)(x - √4)=0
=> x+√4 =0 , x - √4 = 0
=> x = -√4 or x = √4

The zeros of given Polynomial are -√4 and √4

we have to verify .

$sum \: \: of \: zeros \: \: ( - \sqrt{4} + \sqrt{4} ) = \frac{0}{1} = \frac{ - ( coefficient \: of \: x)}{coefficient \: \: of \: {x}^{2} } \\ \\ product \: of \: \: zeros = - \sqrt{4} \times \sqrt{4} = \frac{ - 4}{1} = \frac{constant \: \: term}{coefficient \: \: of \: {x}^{2} }$
HENCE verified .

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