Question

if one of the zero of the polynomial p(x)=x²+x+k is 5 then find the value of k

Answer 1

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Answer 2

In the above Question , the following information is given -

One of the zeroes of the polynomial p(x) = x² + x + k is 5.

To find -

Find the value of k .

Solution -

Here ,

One of the zeroes of the polynomial p(x) = x² + x + k is 5.

So ,

p ( x ) = x² + x + k .

Now ,

As 5 is one of the factors of the given expression ,

Substituting the value , 5 in place of x ,

P ( 5 )

=> 5 ² + 5 + k

=> 25 + 5 + k

=> k + 30 .

Now ,

P ( 5 ) = 0

=> k + 30 = 0

=> k = - 30

So , the required expression becomes -

p ( x ) = x² + x - 30

Zeroes of this Polynomial -

=> x² + x - 30 = 0

=> x² + 6x - 5x - 30 = 0

=> x ( x + 6 ) - 5( x + 6 ) = 0

=> ( x - 5 )( x + 6 ) = 0

Thus ,

Required Zeroes of this polynomial -

=> x = 5 and -6

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Additional information -

Sum of Zeroes of a polynomial

=> Alpha + Beta = [ - b / a ]

Product of Zeroes of a polynomial

=> Alpha × Beta = [ c / a ]

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