Question

find a quadratic polynomial,the sum and product of whose zeroes are -1 and -20 respectively.hence find the zero

Answer 1

Hi ,

We know that ,
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Equation of the polynomial whose

zeroes are p and q is

k(x^2 - ( p + q ) x + pq )

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According to the given problem,

Sum of the zeroes = -1

p + q = - 1 -----( 1 )

Product of the zeroes = - 20

pq = - 20 -----( 2 )

Therefore , required polynomial is

k [ x^2 - ( - 1 ) x + ( -20 )

= k ( x^2 + x - 20)

k is real number ,

Let us assume k = 1,

x^2 + x - 20

ii) Finding zeroes ,

( p - q )^2 = ( p + q )^2 - 4pq

= ( -1 )^2 - 4 ( -20 )

[ from ( 1 ) and ( 2 ) ]

= 1 + 80

= 81

Therefore ,

p - q = + or - 9 -----( 3 )

Add ( 1 ) and ( 3 )

We get p = -5 or 4

Put p values in ( 2 ), we get

q = 4 or -5

If p = - 5 then q = 4

Or

If p = 4 then q = -5

I hope this helps you.

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