Question

The polynomial x2 – 3x + 1 has
A) two linear factors
C) no linear factor
B) only one linear factor
D) more than two linear factors​

Answer 1

b , only one linear factor

Answer 2

$\bf{\underline{Question:-}}$

The polynomial x² – 3x + 1 has

A) two linear factors

C) no linear factor

B) only one linear factor

D) more than two linear factors

$\bf{\underline{Solution:-}}$

• The given polynomial has two factors because variable x has power 2 .

$\bf{\underline{Checking \:the \:factors \:of\: given:polynomial:-}}$

$\sf → x^2 - 3x + 1$

$\bf{\underline{Using\: Quadratic\: Formula}}$

★ x = b² ± √(b - 4ac)/2a

• a = x
• b = -3
• c = 1

$\sf → x = \frac{-(-3) ± \sqrt{-3^2-4×1×1}}{2×1}$

$\sf → x = 3±\frac{9-4}{2}$

$\sf → x = 3 ± \frac{\sqrt{5}}{2}$

$\sf → x = 3 + \frac{\sqrt{5}}{2}$ or

$\sf → x = 3 - \frac{\sqrt{5}}{2}$