Question 1 What is the value of the coefficient "b" when the quadratic
equation y = (3x − 5)(2x + 3) is written in standard form?
19
6
−15
−1
Solution::
(3x -5)(2x + 3) = 6x^2 + 9x - 10x - 15 = 6x^2 - x - 15, then a=6, b=-1 and c= - 15
Answer: b = -1
Question 2 Solve x2 − 4x = 12.
x = −3, x = 4
x = 3, x = −4
x = 6, x = −2
x = −6, x = 2
Solution
x^2 -4x - 12 =0
Factor
(x - 6 )(x + 2 ) = 0
x = 6 and x = -2
Question 3 How many and of what type are the solutions of a quadratic equation when the value of the radicand is 25?
No real solutions
Two identical rational solutions
Two different rational solutions
Two irrational solutions
Answer: two diferent rational solutions.
Question 4 What are the approximate solutions of 3x2 − 5x = 3 rounded to the nearest hundredth?
No real solutions
x ≈ −1.41 and x ≈ 6.41
x ≈ −0.47 and x ≈ 2.14
x ≈ −2.14 and x ≈ 0.47
Solution: use the quadratic formula
[-b +/- √(b^2 - 4ac) ] / 2a
Standard form:
3x2 − 5x - 3 =0, then a =3, b = - 5, and c = -3
Answer: x ≈ −0.47 and x ≈ 2.14
Question 5 How many and of what type are the solutions to x2 + 9x + 10 = 0?
No real solutions
Two identical rational solutions
Two different rational solutions
Two irrational solutions
Solution find the determinant: b^2 - 4ac = 9^2 - 4(1)(10) = 81 - 40 = 41
Then there are two different solutions and they are irrational because √41 is irrational.
Answer: two irrational solutions.
