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Sedbober [7]
3 years ago
5

Find counter example to disprove the conjecture: 

Mathematics
1 answer:
romanna [79]3 years ago
3 0

\frac{  - 2}{ - 1}  = 2
this is an example where the quotient is postive but the two numbers are negative
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What is the sum of the roots of the polynomial shown below?<br> f(x) = x^3 + 2x^2 - 11x-12
svp [43]

<u>Answer:  </u>

Sum of the roots of the polynomial x^{3}+2 x^{2}-11 x-12 \text { is }-2

<u>Solution:</u>

The general form of cubic polynomial is a x^{3}+b x^{2}+c x+d=0 ---- (1)

If we have any cubic polynomial a x^{3}+b x^{2}+c x+d=0 having roots \alpha , \beta , \theta

Sum of roots \alpha + \beta + \theta = \frac{-b}{a} ---(2)

From question given that,

x^{3}+2 x^{2}-11 x-12 --- (3)

On comparing equation (1) and (3), we get a = 1, b = 2, c = -11 and d = -12

Hence the sum of roots using eqn 2 is given as,

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Hence the sum of the roots of the polynomial x^{3}+2 x^{2}-11 x-12 \text { is }-2

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3 years ago
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