Obtain the discriminant of the equation 2x³ - 23x²+82x-78=0. Hence provide the nature of its roots.
The discriminant (\(\Delta\)) of a cubic equation of the form: \[ ax^3 + bx^2 + cx + d = 0 \] is given by the formula: \[ \Delta = 18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2 \] ### Step 1: Identify the coefficients For the given equation: \[ 2x^3 - 23x^2 + 82x - 78 = 0 \] we have: - \( a = 2 _____ _______ _______ _________ _________.
_________ ___ ____ ________ _____ ___ __________ ________ __________ ___.
__________ _____ _____ ____ ________.
____ _________ ______ _________ ___.
_________ _______ _____ __________ _________ ____ ______.
_______ _____ _____ ______ _________ _______ ___ __________ ________.
________ __________ ________ ________ __________ _______ ________.
_______ __________ ______ _________ ___ _________ _____ ________ __________ ______ _____ ___.
____ _____ ___ ________ _________ ____ ______ __________ ____.
______ ____ ________ _____ ________ ______ _______ ____ ______.
_______ ___ _____ _________ ________ _____ _________ ____.
_____ _____ __________ __________ ________ ______ __________ _________ ____ _______.
___ ________ ___ ___ ________ ________ ______ ____ ____ ____.
___ __________ ________ ______ ___ _________ _______ __________ _____ _________.
____ ____ _____ _______ __________ _____ ________ ___ ___ ________.
__________ _____ _______ ______ ________ _______ ____ ___ __________ _______ ____.
_________ ____ _____ ______ ________ __________ ____.
____ __________ _________ ______ ___ ________ ____ _________ ________ _________.
________ _______ _________ ____ ___ ___ _______ _______ _______ _____ _____.
___ ____ ________ _____ ___ ___ ____ _____ ___ _______ __________.
___ _______ __________ _________ ____ ___ _______ ____ ________.
_______ _________ __________ _____ ______ ______ _________ ________ _________ ____ ________ ___.
________ ___ _____ __________ _______ _________ _________ ____ _______ _________ _________ _____.
____ ___ ______ _______ _____ ________.
_________ ___ _________ __________ _________ ___ __________ ______ ______ ________ ___ ________.
____ _________ _____ _________ __________ ____ ___ ___ ___.
___ ______ ____ _______ __________ ___ _______ ________.
________ _____ ______ __________ _____ ________ _______ _________ _______ _______.
___ _______ _________ ___ ________ _________ ________.
______ ____ _____ __________ ______ ________ _________.
Get Full Answer on WhatsApp
Let x such that
Express in standard (algebraic) form. Further, give an Argand diagram
in which and
are plotted
सिद्ध कीजिए कि जहां एक्स, x, y, z > 0 .
Obtain the polar and exponential representations of where
Is Cramer's Rule applicable for solving the linear system below? If yes, apply it. Otherwise, alter the last equation in the system so that the solution can be obtained by applying the Rule.
x + y + z = π
– πχ + π + √2z = 0
π²x + π²y + 2z = 0.
न्यूनतम घात वाला पर एक बहुपद ज्ञात कीजिए जिसके मूल i - 2 और हों।
Which of the following statements are true? Justify your answers. (This means that if you think a statement is false, give a short proof or an example that shows it is false. If it is true, give a short proof for saying so. For instance, to show that "{1, padma, blue) is a set' is true, you need to say that this is true because it is a well-defined collection of 3 objects.)
i) The collection of Venn diagrams is a set.
ii) for any three sets B,A and C .
iii)
iv) , has a root in R only if m is an odd number.
v)
vi) Any system of three linear equations in two variables has no solution
vii) If a matrix has 2 n entries, where n ∈ N , then it is a square matrix.
viii) For n > 4 , the AM of the first n natural numbers is greater than n +1