Question

Q Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively.​

Answer 1

Answer:

Step-by-step explanation:

We know that ,

___________________________

Equation of the polynomial whose

zeroes are p and q is

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

________________________

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.

Answer 2

hey matw:

given here

sum if zeroes = 4

and ,

product of zeroes = 1

quadratic equation

x^2-(sum of zeroes )x + (products of zeroes)= 0

so,

x^2 - (4)x+1=0.

i hopes its helps u.

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@abhi.