Hello,
P(x)=x^4-6x²+2=(x-a)(x-b)(x-c)(x-d)
=x^4-(a+b+c+d)x^3+(ab+ac+ad+bc+bd+cd)x^2-(abc+abd+acd+bcd)x+abcd
==>
ab+ac+ad+bc+bd+cd=-6
abc+abd+acd+bcd=0
abcd=2
a+b+c+d=0 ==>(a+b+c+d)²=0=a²+b²+c²+d²+2(ab+ac+ac+bc+bd+cd)
==>a²+b²+c²+d²=0-2*(-6)=12
if a is a root P(a)=0==>a^4-6a²+2=0
if b is a root P(b)=0==>b^4-6b²+2=0
if c is a root P(a)=0==>c^4-6c²+2=0
if d is a root P(a)=0==>d^4-6d²+2=0
==>a^4+b^4+c^4+d^4-6(a²+b²+c²+d²)+4*2=0
==>a^4+b^4+c^4+d^4=-8+6*12=64
Answer:
30
Step-by-step explanation:
5(z+4)+5(2-z) (expand parentheses by distribution)
= z(5) + 4(5) + 2(5) -z(5)
= 5z + 20 + 10 -5z
= 30
Answer:
18) Area= 5*5/2=25/2=12.5 unit ^2
19) Area=AB^2V3/4=8a^2*V3/4=2V3a^2
Step-by-step explanation:
18. A(-3,0)
B(1,-3)
C(4,1)
AB=V(-3-1)^2+(0+3)^2=V16+9=V25=5
AC=V(-3-4)^2+(0-1)^2=V49+1=V50=5V2
BC=V(1-4)^2+(-3-1)^2=V9+16=V25=5
so AB=BC=5
and AC^2=AB^2+BC^2
so trg ABC is an isosceles right angle triangle (<B=90)
Area= 5*5/2=25/2=12.5 unit ^2
19. A(a,a)
B(-a,-a)
C(-V3a, V3a)
AB=V(a+a)^2+(a+a)^2=V4a^2+4a^2=V8a^2
AC=V(a+V3a)^2+(a-V3)^2=Va^2+2a^2V3+3a^2+a^2-2a^2V3+3a^2=V8a^2
BC=V(-a+V3a)^2+(-a-V3a)^2=V8a^2
so AB=AC=BC
Area=AB^2V3/4=8a^2*V3/4=2V3a^2
100 because 40% is 40 and you do not kno the exact number of apples
The theoretical probability is 25% for each section
