Find the roots of the cubic equation $2 x^{3} - x^{2} - 50 x + 25 = 0$

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Solution

$2 x^{3} - x^{2} - 50 x + 25 = 0$
$x^{2} (2 x - 1) - 25 (2 x - 1) = 0$
$(x^{2} - 25) (2 x - 1) = 0$
$(x - 5) (x + 5) 2 (x - \frac{1}{2}) = 0$
$∴ x = 5, - 5, \frac{1}{2}$

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Find the roots of the cubic equation 2x3−x2−50x+25=0

2x3−x2−50x+25=0x2(2x−1)−25(2x−1)=0(x2−25)(2x−1)=0(x−5)(x+5)2(x−12)=0∴x=5,−5,12

Find the roots of the cubic equation $2 x^{3} - x^{2} - 50 x + 25 = 0$

$2 x^{3} - x^{2} - 50 x + 25 = 0$
$x^{2} (2 x - 1) - 25 (2 x - 1) = 0$
$(x^{2} - 25) (2 x - 1) = 0$
$(x - 5) (x + 5) 2 (x - \frac{1}{2}) = 0$
$∴ x = 5, - 5, \frac{1}{2}$