Question

Define quadratic polynomial with real coefficients

Answer 1

Answer:

A polynomial having only one number as coefficients.

Explanation:

A polynomial with real coefficients is the product of irreducible polynomials of first and second degrees

Answer 2

$\huge\sf\underline{\purple{❥}\pink{Q}\orange{U}\blue{E}\red{S}\green{T}\purple{I}\pink{O}\red{N}}$

Define quadratic polynomial with real coefficients.

$\huge\sf\underline{\purple{❥}\pink{A}\orange {N}\blue{S}\red{W}\green{E}\purple{R}}$

$\color{red}{About \:Quadratic \: polynomials\: :-}$

➯ A polynomial having degree 2 is called a quadratic polynomial.

➯ The form of quadratic polynomial is

$p(x) = a {x}^{2} + bx + c$

➯ Degree of the quadratic polynomial will be 2.

➯ Variable of the quadratic polynomial will be 1.

$\color{red}{For \:example :-}$

$p(x) = 2 {x}^{2} + 5x + 3 \\ 3 \:➝ \: constant \\ 2 \: and \: 5 \: ➝ \: coefficient \\ {}^{2} \: ➝ \: degree \\ x \:➝ \: variable \:$

➯ In a quadratic polynomial there are 2 zeros because it has degree 2.

$\color{red}{➯ The \: 2\: zeros \:are :-}$

$i) \: \: alpha( \alpha ) \: \\ ii) \: beta \: ( \beta )$

$\color{red}{For \:example :-}$

$p(x) = 2 {x}^{2} + 5 + 3 \\ = 2 {x}^{2} + 2x + 3x + 3 \\ = 2x(x + 1) + 3(x + 1) \\ = (x + 1)(2x + 3) \\ \\ As, \: \: p(x) = 0 \\ \\ ❥∴ \: (x + 1)(2x + 3) = 0 \\ x + 1 = 0 \\ x = - 1 \\ \\ ❥ \: 2x + 3 = 0 \\ 2x = - 3 \\ x = \frac{ - 3}{2} \\ \\ Here, \: \alpha = - 1 \\ \beta = \frac{ - 3}{2}$