Question

simplify (x squared -7x+2)(x squared +5x-4)​

Answer 1

Given the polynomial;

• (x² - 7x + 2)(x² + 5x - 4)

Thus for ( x² - 7x + 2) ;

• a = 1
• b = -7 { onpared with standard quadratic polynomial ax² + bx + c}
• c = 2

Therefore D = b²-4ac

• D = (-7)² - 4(1)(2)
• D = 49 - 8
• D = 41

Using he quadratic formula ; roots = (-b ± √D)/ 2a

{ let α & β be it's roots }

• α = -(-7) + √41/ 2(1)
• α = (7 + √41 )/ 2

• β = -(-7) -√41 / 2(1)
• β = (7-√41 )/ 2

Thus for ( x² + 5x - 4)

• a = 1
• b = 5
• c = -4

Therefore D = b²-4ac

• D = (5)² - 4(1)(-4)
• D = 25 + 16
• D = 41

Using the quadratic formula ; roots = (-b ± √D)/2a

{let γ & δ be it's roots}

• γ = -5 + √41 / 2(1)
• γ = (-5 + √41 )/ 2

• δ = -5 - √41 / 2(1)
• δ = (-5 - √41 )/ 2

Thus the roots of the above polynomial are

• x = α = (7 + √41 )/ 2 => (2x - 7 - √41 ) = 0. { factor form }
• x = β = (7-√41 )/ 2 => (2x - 7 + √41 ) = 0
• x = γ = (-5 + √41 )/ 2 => (2x + 5 - √41) =0
• x = δ = (-5 - √41 )/ 2 => ( 2x + 5 + √41) = 0

Thus simplified form ;

(2x -7 -√41)(2x -7 + √41)(2x + 5 - √41)(2x + 5+ √41)

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