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If all the zeros of a …

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If all the zeros of a cubic polynomial are negative , then all the coefficients and constant term of the polynomial have the same sign. State true or false and justify your answer.

Posted by Tiyas Dutta 6 years, 7 months ago

CBSE > Class 10 > Mathematics

3 answers

Diksha Chawla 6 years, 7 months ago

Say three zeroes are -a, -b, -c. Then factors become (x+a),(x+b),(x+c) The polynomial become =(x+a)(x+b)(x+c) =(x^2+(a+b)x+ab)(x+c) =(x^3+(a+b+c)x^2+(ab+ac+bc)x+abc Which shows that all coefficients and constant have the same sign. So, Statement is true

2Thank You

Tiyas Dutta 6 years, 7 months ago

Thnx but can you plz justify it

0Thank You

Panchal Akshu 6 years, 7 months ago

True

2Thank You

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CBSE > Class 10 > Mathematics