Question

if a b c and d are the roots of the polynomial equation (x2-3x+4)(x2+2x+5)=0 then the quadratic equation whose roots are a+b+c+d and abcd is

Answer 1

Answer:

please find the attachment.

Answer 2

Answer:

x^2-21x+20=0

Step-by-step explanation:

x^2-3x+4=0- The roots of this quadratic are a,b.

a+b=3(sum of roots)-(1)

ab=4(product of roots)-(2)

x^2+2x+5=0- The roots of this quadratic are c,d.

c+d= -2-(3)

cd=5-(4)

For the required quadratic, the roots are

a+b+c+d=(1)+(3)=1=k

abcd=(2)*(4)=20=l

the structure of a quadratic equation is

x^2-(sum of roots)x+(product of roots)=0

x^2-(k+l)x+(kl)=0

x^2-(1+20)x+(20*1)=0

Ans: x^2-21x+20=0