USING DISCRIMINANT WORKSHEET

Examine the nature of the roots of the following quadratic equations.

Question 1 :

x² + 5x + 6 = 0

Question 2 :

2x² - 3x + 1 = 0

Question 3 :

x² - 16x + 64 = 0

Question 4 :

3x² + 5x + 8 = 0

Question 5 :

If the roots of the equation 2x² + 8x - m³ = 0 are equal , then find the value of m.

1. Answer :

Comparing

ax² + bx + c = 0

and

x² + 5x + 6 = 0,

we get a = 1, b = 5 and c = 6.

Find the value of the discriminant 

Δ = b² - 4ac

Δ = 5² - 4(1)(6)

Δ = 25 - 24

Δ = 1 > 0

Hence, the roots are real and unequal.

2. Answer :

Comparing

ax² + bx + c = 0

and

2x² - 3x + 1 = 0,

we get a = 2, b = -3 and c = 1.

Find the value of the discriminant.

Δ = b² - 4ac

Δ = (-3)² - 4(2)(-1)

Δ = 9 + 8

Δ = 17 > 0

Hence, the roots are real and unequal.

3. Answer :

Comparing

ax² + bx + c = 0

and

x² - 16x + 64 = 0,

we get a = 1, b = -16 and c = 64.

Find the value of the discriminant 

Δ = b² - 4ac

Δ = (-16)² - 4(1)(64)

Δ = 256 - 256

Δ = 0

Hence, the roots are real and equal.

4. Answer :

Comparing

ax² + bx + c = 0

and

3x² + 5x + 8 = 0,

we get a = 3, b = 5 and c = 8.

Find the value of the discriminant 

Δ = b² - 4ac

Δ  = 5² - 4(3)(8)

Δ  = 25- 96

Δ = -71 < 0

Hence, the roots are imaginary.

5. Answer :

Comparing

ax² + bx + c = 0

and

2x² + 8x - m³ = 0,

we get a = 2, b = 8 and c = -m³.

Since the roots are equal, we have Δ = 0

x² - 4ac = 0

8² - 4(2)(-m³) = 0

64 + 8m³ = 0

8m³ = -64

m³ = -8

m³ = (-2)³

m = -2

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