Let f(x)=x^4+a x^3+b x^2+c be a polynomial with real coefficients such that f(1)=-9. Suppose that i 3 is a root of the equation 4 x^3+3 a x^2+2 b x=0, where i= -1 . If _1, _2, _3, and _4 are all the roots of the equation f(x)=0, then | _1 |^2+ | _2 |^2+ | _3 |^2+ | _4 |^2 is equal to ________.
A. A
f(1)=1+a+b+c=-9 a+b+c=-10.....(1) 4 x^3+3 a x^2+2 b x=0 roots are 3 i,- 3 i, 0 4 x^2+3 a x+2 b=0 < ^ 3i _ - 3i a =0 ~\&~ 2 ~b 4 =( 3 i )(- 3 i ) b =6 use a , b in (1) c =-16 array ll & f ( x )= x ^4+6 x ^2-16=0 \\ & ( x ^2+8 ) ( x ^2-2 )=0 \\ & x = 8 i , 2 array | _1 |^2+ | _2 |^2+ | _3 |^2+ | _4 |^2=20
Related: Mathematics — Quadratic Equation · All PYQ Banks