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Question
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
Options
Both Assertion (A) and Reason (R) are true and Reason (R) gives the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) does not give the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Solution
Assertion (A) is true but Reason (R) is false.
Explanation:
Assertion: We have,
4x2 – 10x + (k – 4) = 0
Product of zeroes = 1
So, `("k" - 4)/4` = 1
k = 8
Assertion is correct.
Reason: For quadratic equation, x2 – x + 1 = 0
We have, Discriminant = (–1)2 – 4 = –3 < 0
So, no real roots are possible.
Reason is incorrect.
Hence, Assertion is correct and reason is incorrect.
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