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# EXPLAIN your answer! 34- If a is a root of x^3 + rx^2 +sx + t-0- th.docx

EXPLAIN your answer! 34. If a is a root of x^3 + rx^2 +sx + t=0, then a is a factor of t. 35. Sq. root of 5 and -Sq.rooot of 5 are roots of x^3 + rx^2 + sx + t= 0. 36. 2+i and -2-i are roots of ^3 + rx^2 + sx + t= 0. Please do all of them if you can. Thanks.
Solution
34. It is a third degree polynomial. So it has three roots. Let them be a,b,c. Then product of roots = t/1 =>abc = t =>a is a factor of t.....Always true. 35.Sometimes true since it depends on the values of r,s,t 36.Never true. Since if (2+i) is a root then (2-i) also has to be a root. And if -2-i is a root then -2+i also has to be a root. But then it becomes fourth degree polynomial. And we have third degree polynomial. So it is never true.
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EXPLAIN your answer! 34. If a is a root of x^3 + rx^2 +sx + t=0, then a is a factor of t. 35. Sq. root of 5 and -Sq.rooot of 5 are roots of x^3 + rx^2 + sx + t= 0. 36. 2+i and -2-i are roots of ^3 + rx^2 + sx + t= 0. Please do all of them if you can. Thanks.
Solution
34. It is a third degree polynomial. So it has three roots. Let them be a,b,c. Then product of roots = t/1 =>abc = t =>a is a factor of t.....Always true. 35.Sometimes true since it depends on the values of r,s,t 36.Never true. Since if (2+i) is a root then (2-i) also has to be a root. And if -2-i is a root then -2+i also has to be a root. But then it becomes fourth degree polynomial. And we have third degree polynomial. So it is never true.
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