Let a, b, c be real numbers such that `ax^(2) + bx + c = 0 and x^(2) + x + 1 = 0` have a common root.
Statement-1: a = b = c
Staement-2: Two quadratic equations with real coefficients cannot have only one imainary root common.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

A

Explanation

The equation `x^(2) + x + 1 = 0` has imaginary roots `omega and omega^(2). If ax^(2) + bx + c = 0 and x^(2) + x + 1 = 0` has one imaginary root common, then other imaginary root must also be common as imaginary roots occur in pairs. So, statement-2 is true.
Given equations have both roots common.
`therefore" "(a)/(1)=(b)/(1)=(c)/(1) rArr a = b = c`
So, statement-1 is also true and statement-2 is a correct explanation for statement-1.