PDF chapter test TRY NOW
Abraham bar Hiyya Ha-Nasi, also known as Savasorda, was an Arab mathematician famous for his book "Liber Embadorum," published in 1145 \ AD(CE) and was the first book in Europe to present the complete solution to the quadratic equation.
Quadratic expression
The polynomial is an expression of degree n for the variable x is of the form p(x) = a_0 x^n + a_{1}x^{n-1} + … + a_{n -1}x + a_n, where a_0, a_1, a_2, …, a_n are coefficients and a_0 \ne 0.
A quadratic expression is a polynomial of degree 2 for the variable x is of the form p(x) = ax^2 + bx + c, a \ne 0 and a, b and c are real numbers.
Example:
1. Check p(x) = (x - 4)^3 + 4x + 2 is a quadratic expression.
Solution:
p(x) = (x - 4)^3 - 4x + 2
= x^3 - 12x^2 + 48x - 64 - 4x + 2 [Using the identity (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3]
= x^3 - 12x^2 + 44x - 62
Here, the degree of the equation is 3.
Thus, the given equation is not a quadratic expression.
2. Check p(x) = (x + 2)^3 - x^3 + 3 is a quadratic expression.
Solution:
p(x) = (x + 2)^3 - x^3 + 3
= x^3 + 6x^2 + 12x + 8 - x^3 + 3 [Using the identity (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3]
= 6x^2 + 12x - 11
Here, the degree of the polynomial is 2.
Thus, the given equation is a quadratic expression.