For the quadratic equation x^2 + (-4)x + -2 = 0, determine the nature of its roots.
Correct answer(s):
- two distinct real roots
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For the quadratic equation x^2 + (-5)x + -3 = 0, determine the nature of its roots.
Correct answer(s):
- two distinct real roots
For the quadratic equation x^2 + (-6)x + -4 = 0, determine the nature of its roots.
Correct answer(s):
- two distinct real roots
For the quadratic equation x^2 + (-7)x + -5 = 0, determine the nature of its roots.
Correct answer(s):
- two distinct real roots
For the quadratic equation x^2 + (-8)x + -6 = 0, determine the nature of its roots.
Correct answer(s):
- two distinct real roots
For the quadratic equation x^2 + (-9)x + -7 = 0, determine the nature of its roots.
Correct answer(s):
- two distinct real roots
For the quadratic equation x^2 + (-10)x + -8 = 0, determine the nature of its roots.
Correct answer(s):
- two distinct real roots
For the quadratic equation x^2 + (-11)x + -9 = 0, determine the nature of its roots.
Correct answer(s):
- two distinct real roots
Select all expressions equal to 9(x + 8).
Correct answer(s):
- 9 × (x + 8)
- 9x + 72
Select all statements true for the equation x^2 – 16x + 64 = 0.
Correct answer(s):
- Sum of roots is 16
- Product of roots is 64
Select all values that satisfy x^2 = 25.
Correct answer(s):
- 5
- -5
Select all correct factors of x^2 – 4.
Correct answer(s):
- x + 2
- x - 2
Select all expressions equivalent to (x + 6)^2.
Correct answer(s):
- x^2 + 12x + 36
- (x + 6)(x + 6)
Five times a number decreased by 7 equals 103. Which equation solves the problem?
Correct answer(s):
- 5x - 7 = 103
7 identical pens cost 210 taka. If one pen costs x taka, which equation and value are correct?
Correct answer(s):
- 7x = 210, x = 30
A rectangle has perimeter 72 cm and length 2 cm more than its width. Find its width.
Correct answer(s):
- 17 cm
A father’s age is 4 more than three times his son’s age. If the father is 73, find the son’s age.
Correct answer(s):
- 23
Two numbers have sum 43. The larger number is 5 more than the smaller. Find the smaller number.
Correct answer(s):
- 19
A number is doubled and 5 is added. The result is 39. What is the number?
Correct answer(s):
- 17
Five times a number decreased by 7 equals 78. Which equation solves the problem?
Correct answer(s):
- 5x - 7 = 78