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05 Feb 2020, 03:31
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E
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If \(a\) and \(-a\) are the roots of the equation \(2x^3 − 5x^2 − 8x + n = 0\), what is the value of \(n\)?
A. -25
B. -20
C. -10
D. 10
E. 20
Are You Up For the Challenge: 700 Level Questions
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A. -25
B. -20
C. -10
D. 10
E. 20
Are You Up For the Challenge: 700 Level Questions
[/textarea]
shameekv1989
05 Feb 2020, 04:16
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If a and -a are the roots of the equation \(2x^3−5x^2−8x+n=0\), what is the value of n?
A. -25
B. -20
C. -10
D. 10
E. 20
Substituting value a and -a in the equation :-
\( 2a^3−5a^2−8a+n=0\) --- i)
\(-2a^3−5a^2+8a+n=0\) ---ii)
Adding -> \(2n = 10a^2\) -> \(n = 5a^2\)
Substituting back in i) \( 2a^3−5a^2−8a+5a^2=0\) -> \( 2a^3−8a=0\) -> a=0; a=2; a=-2
Therefore \(n = 5a^2 = 5*4 = 20\) - Answer - E
A. -25
B. -20
C. -10
D. 10
E. 20
Substituting value a and -a in the equation :-
\( 2a^3−5a^2−8a+n=0\) --- i)
\(-2a^3−5a^2+8a+n=0\) ---ii)
Adding -> \(2n = 10a^2\) -> \(n = 5a^2\)
Substituting back in i) \( 2a^3−5a^2−8a+5a^2=0\) -> \( 2a^3−8a=0\) -> a=0; a=2; a=-2
Therefore \(n = 5a^2 = 5*4 = 20\) - Answer - E
05 Feb 2020, 09:26
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Bunuel
If \(a\) and \(-a\) are the roots of the equation \(2x^3 − 5x^2 − 8x + n = 0\), what is the value of \(n\)?
A. -25
B. -20
C. -10
D. 10
E. 20
A. -25
B. -20
C. -10
D. 10
E. 20
if g and -g are roots of equation: 2x^3-5x^2-8x+n=0;
then you can subs g with x or -g with x, and both must return 0;
solving for n:
\([1]: 2g^3-5g^2-8g+n=0\)
\([2]: 2(-g)^3-5(-g)^2-8(-g)+n=0……2g^3-5g^2+8g+n=0\)
\([1+2]:-10g^2+2n=0, n=5g^2\)
\([sub.n]: 2g^3-5g^2-8g+n=0…2g^3-5g^2-8g+5g^2=0\)
\(…2g^3-8g=0 …2g(g^2-2^2)=0…2g(g+1)(g-1)=0…g=(-1,1)\)
\([sub.g]: n=5g^2… n=5({-1,1})^2=20\)
Ans (E)
