Find roots 'a' and 'b' of the quadratic equation 2(x^2) + 6x + 7 = 0
We know to find roots of any quadratic equation we use the quadratic formula, [-b +- (b^2 - 4ac)^(1/2)]/2a where a=2, b=6, and c=7.
Plug these values in and we obtain, [-6 +- (-20)^(1/2)]/4. [Remember for imaginary numbers, (-a)^(1/2) = (a^(1/2))*((-1)^(1/2)) = a^(1/2) *i.]
So we have, [-6 +- 25^(1/2)i]/4 since 20^(1/2) = (45)^(1/2) = 25^(1/2). Therefore, our two roots are
a = (-3/2) + [5^(1/2)/2]*i b = (-3/2) - [5^(1/2)/2]*i
SN
Answered by Sam N. • Further Mathematics tutor
3883 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Find the GS to the following 2nd ODE: d^2y/dx^2 + 3(dy/dx) + 2 = 0
Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)
Find the equation of the tangent to the curve y = exp(x) at the point ( a, exp(a) ). Deduce the equation of the tangent to the curve which passes through the point (0,1) .
Let A, B and C be nxn matrices such that A=BC-CB. Show that the trace of A (denoted Tr(A)) is 0, where the trace of an nxn matrix is defined as the sum of the entries along the leading diagonal.