Homework 2:
1. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes
respectively. Find the zeroes of these polynomials by factorisation.
Answers
Answer:
Step-by-step explanation:
(i)
4
1
, -1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−
4
1
x−1=0
4x
2
−x−4=0
(ii)
2
,
3
1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−
2
x+
3
1
=0
Multiply by 3 to remove denominator,
3x
2
−3
2
x+1=0
(iii) 0,
5
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−0x+
5
=0
x
2
+
5
=0
(iv) 1, 1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−1x+1=0
x
2
−x+1=0
(v)
4
−1
,
4
1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−
4
−1
x+
4
1
=0
Multiply by 4
4x
2
+x+1=0
(vi) 4, 1
Using the quadratic equation formula,
x
2
−(Sum of root)x+(Product of root)=0
Substitute the value in the formula, we get
x
2
−4x+1=0