Question

Find a quadratic polynomial, the sum and product of whose zeroes are ─ 3 and 2 , respectively. *

1 point

(a) x^2+ 3x+2

(b) x^2- 3x+2

(c) x^2+ 3x-2

(d) x^2- 3x-2

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Answer 1

Answer:

option A : x^2+3x+2

Step-by-step explanation:

the quadratic whose zeroes are 'm' and 'n'

is x^2-(m+n)x+mn

so quadratic whose sum of zeroes is 'a'. (a=m+n) and product of zeroes is 'b'. (b=mn)

is, x^2-ax+b

given, a= -3 and b=2

so the quadratic is x^2-(-3)x+2 => x^2+3x+2

(this is one method ( I personally find this more easy))

or another method is

given , sum of roots = -3 and product of roots = 2

let the roots be 'c' and 'd'

then , c+d= -3 , cd=2

from c+d= -3 we can say that d= -3-c so

cd=2 => c(-3-c)=2

=> c^2+3c= -2

=> c^2+3c+2=0

=> c^2+c+2c+2=0

=> c(c+1)+2(c+1)=0

=> (c+1)(c+2)=0

=> c= -1,-2

so, c= -1 and d= -2 or c= -2 and d= -1

so the quadratic will be x^2- ((-1)+(-2))x+(-1)(-2)

which is, x^2-(-3x)+2 = x^2+3x+2

option A .

hope it helps

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