Question

Write a quadratic polynomial whose zeroes are 3 and −5 and write a quadratic polynomial whose sum and product of the zeroes are −3 and 2 respectively.

Answer 1

Answer:

Step-by-step explanation:

(i) x²+2x-15=0

(ii) x²+x-6=0

(i) Sum of zeroes=3+(-5)=(-2)

 Product of zeroes=(3)(-5)=(-15)

Skeletal Quadratic Equation:-

x²-(sum of roots)x+(product of roots)=0

x²-(-2)x+(-15)=0

x²+2x-15=0

(ii) Sum of roots=(-3)+2=(-1)

  Product of roots=(-3)×(2)=(-6)

Skeletal Quadratic Equation:-

x²-(sum of roots)x+(product of roots)=0

x²-(-1)x+(-6)=0

x²+x-6=0

Answer 2

Answer:

1) alpha = 3

beta = -5

alpha + beta = 3+(-5) = 3-5 = -2

alpha × beta = 3(-5) = 3×(-5) = -15

x²-(alpha+beta)x+(alpha × beta)

x²-3x+(-15)

x²-3x-15

2) alpha = -3

beta = 2

alpha + beta = -3+2 = -1

alpha × beta = -3(2) = -3×2 = -6

x²-(alpha+beta)x+(alpha × beta)

x²-(-1)x+(-6)

x²+x-6