Relationship between zeros and coefficients MCQs

Q1. If alpha, beta are zeros of x^2 - 5x + 6, then alpha + beta is (NCERT):

• A.5
• B.-5
• C.-6
• D.6

Answer: A. 5

Given 2, 5, 6, asked for the unknown. By apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation. apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation → so the required value = 5. substitute the coefficients and simplify. Hence option A) 5. Others fail: option B) '-5' is wrong because Sum = -b/a = 5; option C) '-6' fails since Sum is 5.

Q2. If one zero of x^2 - 4x + k is 1, then k is (NCERT):

• A.4
• B.3
• C.-3
• D.1

Answer: B. 3

Q3. If the zeros of a quadratic are reciprocals of each other, then (for ax^2+bx+c) (NCERT):

• A.a = b
• B.b = c
• C.a = c
• D.a = -c

Answer: C. a = c

Given 2, asked for the unknown. By apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation. apply the quadratic formula x = (-b +/- sqrt(b^2 - 4ac))/(2a) to the given equation. substitute the coefficients and simplify. Thus option C) a = c. Others fail: option A) 'a = b' misses the point - Product of zeros = c/a = 1 => a=c; option B) 'b = c' fails since Reciprocal zeros => product 1 => c=a.