Let f(x)=25x^2+kx+2,where k is real.

huangwusheng2022-10-04 11:39:542条回答

Let f(x)=25x^2+kx+2,where k is real.
(a) If f(x)=0 has equal roots,find the value(s) of k,leaving your answer(s) in simplest surd form.(3marks)
(b) If a is the smaller positive root of the quadratic equation f(x)=0,and one root is half of the other,express,in term of a,
(i) the larger root,
(ii) the product of the roots.
Hence find the roots of the equation and the value of k.(5marks)

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ryanhccc 共回答了16个问题 | 采纳率93.8%: (a) f(x)=25x^2+kx+2=0 has equal roots
delta=k^2-4*25*2=0 k=±10√2
(b) one root is half of the other
hence the larger root is double of the smaller root a
(i) 2a
(ii) 2a^2
a*2a=2/25
a is positive
a=1/5 2a=2/5
1/5+2/5=-k/25
k=-15
the two roots are 1/5 and 2/5
k is -15; 1年前

HNZYZYX 共回答了13个问题 | 采纳率: (a) 要有相等的跟，则b^2-4ac=0,代入，即k^2-4*25*2=0,k=10√2.
(b) 把a及a/2代入方程，得25a^2+ka+2=0, (1)
25*(a/2)^2+k*a/2+2=0 (2)
根据方程(1),(2)，解出a=0.4,k=-25或a=-0.4,k=25
根的最大值为0.4。; 1年前

Let f(x)=25x^2+kx+2,where k is real.

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