The coefficients p,q of the expression x 4 + px 3

Question

The coefficients p,q of the expression x4 + px3 + (q+1)x2 + px + q are drawn from the set {1,2,3,4,5,6}. Find the number of ways in which it can be done so that the expression is positive for all real x.

Aditya Gupta · Accepted Answer

The expression can be factored as(x^2+1)(x^2+px+q)So for this to be always positive, x^2+px+q needs to be always positive. That means the discriminant must be less than zero.Or p^2 less than 4q.When p is 1, q can take all 6 values.When p is 2, q can take 5 values.When p is 3, q can take 4 values.When p is 4, q can take 2 values.When p is 5 or 6, q can not take any value.So total number of ways to select p and q is:6+5+4+2=17

Algebra> The coefficients p,q of the expression x ...

The coefficients p,q of the expression x⁴ + px³ + (q+1)x² + px + q are drawn from the set {1,2,3,4,5,6}. Find the number of ways in which it can be done so that the expression is positive for all real x.

Rajesh , 7 Years ago

Aditya Gupta

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Algebra> The coefficients p,q of the expression x ...

The coefficients p,q of the expression x4 + px3 + (q+1)x2 + px + q are drawn from the set {1,2,3,4,5,6}. Find the number of ways in which it can be done so that the expression is positive for all real x.

Rajesh , 7 Years ago

Aditya Gupta

LIVE ONLINE CLASSES

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