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
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