Find a value of c such that the roots of x^2 + 2x +c = 0 are:
a. equal and rational.
b. unequal and rational.
c. unequal and irrational.
d. not real numbers.
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Step-by-step explanation:
ANSWER
For equation x
2
+2x+3=0
Δ=2
2
−4(1)(3)=4−12=−8<0 so both roots are imaginary .
Hence, the roots are non-real. They will exist in complex conjugate pairs.
As one of the roots is common to ax
2
+bx+c=0 , the other root will also be the complex conjugate of it.
Hence, the roots of the two equations will be the same.
Since a, b, c∈R.
If one root is common, then both roots are common .
Hence,
1
a
=
2
b
=
3
c
a:b:c=1:2:3
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