Question

What are quadratic polynomials ​

Answer 1

A quadratic polynomial is a polynomial of degree 2. A univariate quadratic polynomial has the form f(x)=a_2x^2+a_1x+a_0. An equation involving a quadratic polynomial is called a quadratic equation. A closed-form solution known as the quadratic formula exists for the solutions of an arbitrary quadratic equation.

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Answer 2

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

What are quadratic polynomials .

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

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

➯ 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.

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

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

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

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