Sample Questions on Discriminant Formula

Question 1. Solve for x: x² = −2x + 2 using discriminant formula.

Solution:

Given: x² = −2x + 2 or,  x² + 2x − 2 = 0

According to discriminant formula, x = 

Here, a = 1,  b = 2, c = −2.

⇒  x = 

⇒  x = 

⇒  x = (−1 + √3),(−1 – √3).

Question 2. Solve for y: 2y² − 8y − 10 = 0 using discriminant formula.

Solution:

Given: 2y² − 8y − 10 = 0

According to discriminant formula, 

Here, a = 2,  b = −8, c = −10.

⇒  y = 

⇒  y = 

⇒  y = 4, −1.

Question 3. Solve for x: 2x² − 7x + 3 = 0 using discriminant formula.

Solution:

Given: 2x² − 7x + 3 = 0

According to discriminant formula, x = 

Here, a = 2,  b = −7, c = 3.

⇒  x = 

⇒  x = 

⇒  x = 3, 1/2.

Question 4. Solve for x: x² − 2x + 3 = 0 using discriminant formula.

Solution:

Given: x² − 2x + 3 = 0

According to discriminant formula, x = 

Here, a = 1,  b = −2, c = 3.

⇒  x = 

⇒  x = 

Since the value of the discriminant is less than zero (D = −8 < 0), the given quadratic equation has no real solution.

Question 5. Solve for x: x² + 5x + 4 = 0 using discriminant formula.

Solution:

Given: x² + 5x + 4 = 0

According to discriminant formula, x = 

Here, a = 1,  b = 5, c = 4.

⇒  x = 

⇒  x = 

⇒  x = -1, -4.

Question 6. Solve for x: 6x² − x − 15 = 0 using discriminant formula.

Solution:

Given: 6x² − x − 15 = 0

According to discriminant formula, x = 

Here, a = 6,  b = −1, c = −15.

⇒  x = 

⇒  x = 

⇒  x = 5/3, −3/2.

Question 7. Solve for x: x² + 4x + 9 = 0 using discriminant formula.

Solution:

Given: x² + 4x + 9 = 0

According to discriminant formula, x = 

Here, a = 1,  b = 4, c = 9.

⇒  x = 

⇒  x = 

Since the value of the discriminant is less than zero (D = −20 < 0), the given quadratic equation has no real solution.

Algebra can be defined as the branch of mathematics which deals with the study, alteration, and analysis of various mathematical symbols. It is the study of unknown quantities, which are often depicted with the help of variables in mathematics. Algebra has a plethora of formulas and identities for the purpose of studying situations involving variables. It also has various sub-branches such as linear algebra, advanced algebra, commutative algebra, etc.