i will post the questions is separate so its easier to see
Quesion 1 (roots of eqns):
NOTE: in this question, a = alpha sign, b = beta sign
the roots of the quadratic eqn 16x^2+ 7x+4=0 are a^2 and b^2
find:
i) 1/b^2
ii) two distinct quadrtic eqns whose roots are a and b
i) beats me. I dunno.
ii) a^2 + b^2 = -(7/16)
(a^2)(b^2) = 1/4
ab = 1/2 or -1/2
When ab = 1/2
(a+b)^2 = 9/16
a+b = 3/4 or - 3/4
when ab = -1/2
(a+b)^2 = 23/16 (reject as it does not have a rational sq.
root)
Therefore,
Coefficient of x term = -1/2
Coefficient of constant = 3/4 or - 3/4
Therefore, eqns are
x^2 - 1/2x + 3/4 = 0 and x^2 - 1/2x - 3/4 = 0
Multiply each by 4
4x^2-2x+3=0 and 4x^2-2x-3 = 0