alleryIf the polynomial p(x) = x² − 5x + 6 is factored as (x − a)(x − b), the values of a and b satisfy a + b = 5 and ab = 6. Hence a and b are:
A1 and 5
B2 and 3
C−2 and −3
D1 and 6
Answer & Solution
Correct answer: B. 2 and 3
1. We need two numbers whose sum is 5 and product is 6.
2. Pairs (1, 4) → product 4, no.
3. Pairs (2, 3) → product 6 and sum 5. Yes.
4. So a = 2, b = 3, giving x² − 5x + 6 = (x − 2)(x − 3).
5. The solutions of p(x) = 0 are therefore 2 and 3.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
Keep practising Real Numbers and Polynomials
Browse all Real Numbers and Polynomials questions for Kerala SSLC (Class 10), or explore more Mathematics topics.
Related questions
Fill the polynomial-factor blanks so each equation is true.Tap TRUE or FALSE for each polynomial / equation statement.Match each second-degree polynomial to its first-degree factorization.Given any polynomial p(x) and any number a, which polynomial is always a factor of p(x) − Which of the following second-degree polynomials cannot be factored into first-degree realThe factorization of 2x² − 7x + 6 into first-degree polynomials is:In the polynomial x² + kx + 6, the value of k that makes x − 1 a factor is:The polynomial x² + 1 has no first-degree factors over the real numbers because: