Question

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
-1 ¹
— —
4 , 4​

Answer 1

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