Question

The Factor of 2x²-7x+1​

Answer 1

Given

• Quadratic polynomial = 2x² - 7x + 1

To find

• Factors of the given polynomial.

Solution

$\tt\longmapsto{Using\: quadratic\: Formula}$

Here,

• a = 2
• b = -7
• c = 1

⠀

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{D = b - 4ac{\bigstar}}}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {D = (-7)^2 - 4(2)(1)}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {D = 49 - 8}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {D = 41}$

⠀

$\underline{\boxed{\tt{x = \dfrac{-b ± \sqrt{D}}{2a}}}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{-(-7) ± \sqrt{41}}{2 \times 2}}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {x = \dfrac{7 ± \sqrt{41}}{4}}$

⠀

$\tt\longmapsto{Roots\: are}$

• $\tt:\implies{x = \dfrac{7 + \sqrt{41}}{4}}$

• $\tt:\implies{x = \dfrac{7 - \sqrt{41}}{4}}$

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