a. For the equation a x 2 + b x + c = 0 ( a ≠ 0 ) , the formula gives the solutions as x = _______________. b. To apply the quadratic formula, a quadratic equation must be written in the form where ______________ a ≠ 0 . c. To apply the quadratic formula to solve the equation 8 x 2 − 42 x − 27 = 0 , the value of a is _____________, the value of b is _____________, and the value of c is __________. d. To apply the quadratic formula to solve the equation 3 x 2 − 7 x − 4 = 0 , the value of −-b is _____________ and the value of the radicand is _______________. e. The radicand within the quadratic formula is _________ and is called the ___________. f. If the discriminant is negative, then the solutions to a quadratic equation will be (real/imaginary) numbers. g. If the discriminant is positive, then the solutions to a quadratic equation will be (real/imaginary) numbers. h. Given a quadratic function f ( x ) = a x 2 + b x + c = 0 , the function will have no x -intercepts if the discriminant is (less than, greater than, equal to) zero.
a. For the equation a x 2 + b x + c = 0 ( a ≠ 0 ) , the formula gives the solutions as x = _______________. b. To apply the quadratic formula, a quadratic equation must be written in the form where ______________ a ≠ 0 . c. To apply the quadratic formula to solve the equation 8 x 2 − 42 x − 27 = 0 , the value of a is _____________, the value of b is _____________, and the value of c is __________. d. To apply the quadratic formula to solve the equation 3 x 2 − 7 x − 4 = 0 , the value of −-b is _____________ and the value of the radicand is _______________. e. The radicand within the quadratic formula is _________ and is called the ___________. f. If the discriminant is negative, then the solutions to a quadratic equation will be (real/imaginary) numbers. g. If the discriminant is positive, then the solutions to a quadratic equation will be (real/imaginary) numbers. h. Given a quadratic function f ( x ) = a x 2 + b x + c = 0 , the function will have no x -intercepts if the discriminant is (less than, greater than, equal to) zero.
Solution Summary: The author explains the quadratic formula for the equation ax2+bx+c=0.
a. For the equation
a
x
2
+
b
x
+
c
=
0
(
a
≠
0
)
, the formula gives the solutions as
x
=
_______________.
b. To apply the quadratic formula, a quadratic equation must be written in the form where ______________
a
≠
0
.
c. To apply the quadratic formula to solve the equation
8
x
2
−
42
x
−
27
=
0
, the value of a is _____________, the value of b is _____________, and the value of c is __________.
d. To apply the quadratic formula to solve the equation
3
x
2
−
7
x
−
4
=
0
, the value of −-b is _____________ and the value of the radicand is _______________.
e. The radicand within the quadratic formula is _________ and is called the ___________.
f. If the discriminant is negative, then the solutions to a quadratic equation will be (real/imaginary) numbers.
g. If the discriminant is positive, then the solutions to a quadratic equation will be (real/imaginary) numbers.
h. Given a quadratic function
f
(
x
)
=
a
x
2
+
b
x
+
c
=
0
, the function will have no x-intercepts if the discriminant is (less than, greater than, equal to) zero.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
A research study in the year 2009 found that there were 2760 coyotes
in a given region. The coyote population declined at a rate of 5.8%
each year.
How many fewer coyotes were there in 2024 than in 2015?
Explain in at least one sentence how you solved the problem. Show
your work. Round your answer to the nearest whole number.
Answer the following questions related to the following matrix
A =
3
³).
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.