Answer:

1.ײ+6×+9=0.

Discriminant: (6)² - 4(1)(9) = 36 - 36 = 0

Nature of the roots: real, rational and equal.

2.ײ+9×+20=0.

Discriminant: (9)² - 4(1)(20) = 81 - 80 = 1

Nature of the roots: real, rational and unequal.

3:2ײ–10×+8=0.

Discriminant: (-10)² - 4(2)(8) = 100 - 64 = 36

Nature of the roots: real, rational and unequal.

4.ײ+5×+10=0.

Discriminant: (5)² - 4(1)(10) = 25 - 40 = -15

Nature of the roots: non-real or imaginary and unequal.

5.ײ+6×+3=0.

Discriminant: (6)² - 4(1)(3) = 36 - 12 = 24

Nature of the roots: real, irrational and unequal.

6.2ײ+6×+4=0.

Discriminant: (6)² - 4(2)(4) = 36 - 32 = 4

Nature of the roots: real, rational and unequal.

7.3ײ–5×=-4=0.

Discriminant: (-5)² - 4(3)(-4) = 25 + 48 = 73

Nature of the roots: real, irrational and unequal.

8.9ײ–6×=-9.

Discriminant: (-6)² - 4(9)(9) = 36 - 324 = -288

Nature of the roots: non-real or imaginary and unequal.

9.10ײ–4×=8.

Discriminant: (-4)² - 4(10)(-8) = 16 + 320 = 336 Nature of the roots: real, irrational and unequal.

10.3ײ–2×–5=0.

Discriminant: (-2)² - 4(3)(-5) = 4 + 60 = 64

Nature of the roots: real, rational and unequal.

Step-by-step explanation: