Question

Determine nature of roots of quadratic equation 2(a^2 +b^2) X^2+2 (a +b)x+1 = 0 OPTIONS Mark for Review ​

Answer 1

Answer:

we can determine the nature of roots of quadratic equations with

b²-4ac>0 then the roots are real and not equal

b²-4ac=0 then the roots are equal and real

b²-4ac<0 then the roots are complex(not real)

a=2(a²+b²), b= 2(a+b), c= 1

b²-4ac=

(2(a+b))²-4(2(a²+b²))(1)=

4(a²+b²+2ab)-8(a²+b²)=

4a²+4b²+8ab-8a²-8b²=

8ab-4a²-4b²(which is less than 0)

that mean D<0

then the roots are complex (not real)

Answer 2

Answer:

The equation has no real roots