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Question
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 5x + 7 = 0
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Solution
x2 - 5x + 7 = 0
Here, a = 1, b = -5 and c = 7
D = b2 - 4ac
⇒ 25 - 4 x 1 x 7.
⇒ 25 - 28
= -3
Since D < 0 roots are imaginary.
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Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
