Rokossolya
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- Oct 25, 2018
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- 2023
Hi! So I have a few questions from the year 12 Cambridge extension 1 book that I can't seem to get!
1) If one root of the equation x3-bx2+cx-d=0 is equal to the product of the other two roots, show that (c+d)2 = d(b+1)2
2) If the zeroes of the cubic y = x3+ax2+bx+c=0 form an arithmatic sequence, show that the point of inflexion lies on the x-axis
3) Consider the cubix polynomial P(x) = ax3+bx2+cx+d, which has zeroes alpha, beta and gamma such that gamma = alpha + beta, show that alpha + beta = - (b/2a)
Thank you!
1) If one root of the equation x3-bx2+cx-d=0 is equal to the product of the other two roots, show that (c+d)2 = d(b+1)2
2) If the zeroes of the cubic y = x3+ax2+bx+c=0 form an arithmatic sequence, show that the point of inflexion lies on the x-axis
3) Consider the cubix polynomial P(x) = ax3+bx2+cx+d, which has zeroes alpha, beta and gamma such that gamma = alpha + beta, show that alpha + beta = - (b/2a)
Thank you!