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:

1)alpha = 3

beta =-5

alpha + beta = -2 =- b /a

alpha× beta = -15 = c/a

therefor on comparing,

a =1

b=2

c= -15

equation= x² + 2x -15

2) sum of zeroes=-3= -b/a

product of zeroes=2=c/a

on comparing,

a=1

b=3

c=2

equation=x²+3x+2

Answer 2

Answer:

(i) x²+2x-15=0

(ii) x²+x-6=0

Explanation:

(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