Answer:
A quadratic polynomial is a type of polynomial that cannot be factored
Examples are;
x^2 + 3x + 5
x^2 + 5x + 7
Step-by-step explanation:
A quadratic polynomial is a type of polynomial which cannot be factored. Just like prime numbers, it only has two factors, 1 and itself.
Hence, a quadratic polynomial does not have rational roots. Its roots are complex and not real
Example are as follows;
(i) x^2 + 3x + 5
(ii) x^2 + 5x + 7
[tex]\huge\sf\underline{\purple{❥}\pink{Q}\orange{U}\blue{E}\red{S}\green{T}\purple{I}\pink{O}\red{N}}[/tex]
# What does it mean if a quadratic polynomial
is prime? Give two examples of quadratic
polynomials that are prime. Now, find a quadratic
polynomial that is prime.
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[tex]\color{red}{About \:Quadratic \: polynomials\: :-}[/tex]
➯ A polynomial having degree 2 is called a quadratic polynomial.
➯ The form of quadratic polynomial is
[tex]p(x) = a {x}^{2} + bx + c[/tex]
➯ Degree of the quadratic polynomial will be 2.
➯ Variable of the quadratic polynomial will be 1.
[tex]\color{red}{For \:example :-}[/tex]
[tex]p(x) = 2 {x}^{2} + 5x + 3 \\ 3 \:➝ \: constant \\ 2 \: and \: 5 \: ➝ \: coefficient \\ {}^{2} \: ➝ \: degree \\ x \:➝ \: variable \:[/tex]
➯ In a quadratic polynomial there are 2 zeros because it has degree 2.
[tex]\color{red}{➯ The \: 2\: zeros \:are :-}[/tex]
[tex]i) \: \: alpha( \alpha ) \: \\ ii) \: beta \: ( \beta )[/tex]
[tex]\color{red}{For \:example :-}[/tex]
[tex]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} [/tex]
