Nature of roots and Sum and Product of a Quadratic Equation

Nature of roots and Sum and Product of a Quadratic Equation

Multiple Choice

1. Which of the following is the discriminant of the quadratic equation: 𝑥²+2𝑥+5=0?

• A. -16

• B. -4

• C. 4

• D. 16

Multiple Choice

2. How many real roots does the quadratic equation 5𝑥²−8𝑥+6=0 have?

• A. 0

• B. 1

• C. 2

• D. 3

Multiple Choice

3. Which of the following quadratic equations has real roots?

• A. 𝑥²+𝑥+1=0

• D. 4+3𝑥²+3x=0

• C. 2𝑥²−6𝑥+6=0

• D. 3𝑥² - 9x +3=0

Multiple Choice

4. The roots of a quadratic equation are imaginary. Which of the following statement is true about the discriminant of equation?

• A. The discriminant is negative.

• B. The discriminant is equal to zero.

• C. The discriminant is positive and a perfect square.

• D. The discriminant is positive and not perfect square.

Multiple Choice

5. The roots of a quadratic equation are 2 and 5.Which of the following statement is true about the discriminant of equation?

• A. The discriminant is negative.

• B. The discriminant is equal to zero.

• C. The discriminant is positive and not perfect square.

• D. The discriminant is positive and a perfect square.

Multiple Choice

6. Given the equation, 4𝑥²+9𝑥−13=0, which of the following is the nature of its roots?

• A. The roots are real, rational and equal.

• B. The roots are imaginary and unequal.

• C. The roots are real, irrational and unequal.

• D. The roots are real, rational, and unequal.

Multiple Choice

7. The discriminant of a quadratic equation is 34. Which of the following is true about its roots?

• A. The roots are real, rational and equal.

• B. The roots are imaginary and unequal.

• C. The roots are real, irrational and unequal.

• D. The roots are real, rational, and unequal.

Multiple Choice

8. What is the value of 𝑡 that will make the roots of the equation 8𝑥²−4𝑡𝑥+3=0 equal?

• A. 𝑡=±6

• B. 𝑡=±96

• C. 𝑡=±√6

• D. 𝑡=±4√6

Multiple Choice

9. Which of the following quadratic equations has rational equal and real roots?

• A. 9−6𝑥+𝑥²=0

• B. 𝑥²+2𝑥+2=0

• C. 𝑥²+4𝑥−21=0

• D. 4𝑥²+12𝑥+10

Multiple Choice

10. What are the value/s of 𝑘 in the quadratic equation 2𝑥²−5𝑥−𝑘=0 whose roots are imaginary?

• A. 𝑘< 25/8

• B. 𝑘<−25/8

• C. 𝑘>−25/8

• D. 𝑘>25/8