Let a, b, c be real such that ax2 + bx + c = 0 and x2 + x + 1= 0 have

1.	Let a, b, c be real such that ax2 + bx + c = 0 and x2 + x + 1= 0 have a common rootStatement–1 : a = b = cStatement–2 : Two quadratic equations with real coefficients can not have only one imaginary root common.(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» Correct option (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1. Explanation: x² + x + 1 = 0 D = – 3 < 0 ∴ x² + x + 1 = 0 and ax² + bx + c = 0 have both the roots common ⇒ a = b = c.

Let a, b, c be real such that ax2 + bx + c = 0 and x2 + x + 1= 0 have a common rootStatement–1 : a = b = cStatement–2 : Two quadratic equations with real coefficients can not have only one imaginary root common.(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»

Correct option (A) Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1.

Explanation:

x² + x + 1 = 0

D = – 3 < 0

∴ x² + x + 1 = 0 and ax² + bx + c = 0 have both the roots common

⇒ a = b = c.

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