The sum of the real roots of the equation∣∣∣∣x−6;−1;2−3xx−3−32xx+2∣∣∣∣=0is equal to610−4The sum of the real roots of the equation∣∣∣∣x−6;−1;2−3xx−3−32xx+2∣∣∣∣=0is equal to610−4∣∣∣∣x−6;−1;2−3xx−3−32xx+2∣∣∣∣=0∣∣∣∣x−6;−1;2−3xx−3−32xx+2∣∣∣∣=0∣∣∣∣x−6;−1;2−3xx−3−32xx+2∣∣∣∣=0∣∣∣∣x−6;−1;2−3xx−3−32xx+2∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣x−6;−1;2−3xx−3−32xx+2x−6;−1;2−3xx−3−32xx+2x−6;−1;xxxx−6;−6;−−6;6−1;−1;−−1;12−3xx−32222−3x−3x−−33xxx−3x−3xx−−33−32xx+2−3−3−−332x2x22xxx+2x+2xx++22∣∣∣∣∣∣∣∣∣∣∣∣==00666666111111000000−4−4−4−4−−44A6666666B1111111C0000000D−4−4−4−4−4−−44?
6
1
0
−4
Solution:
Given∣∣∣∣x−6;−1;2−3xx−3−32xx+2∣∣∣∣=0By expansion, we getx(−3x2+6x)−(−6;)(2x+4−3x+3)+(−1;)(4x+9x)⇒−5x3+30x−30+5x=0⇒−5x3+35x−30=0⇒x3−7x+6=0, All roots are realSo, sum of roots=0