LIVE Course for free

Rated by 1 million+ students
Get app now
+1 vote
61 views
in Polynomials by (20 points)
recategorized by

Find the quadratic polynomial whose sum and product of the zeros are \( \frac{21}{8} \) and \( \frac{5}{16} \) respectively.

Please log in or register to answer this question.

2 Answers

0 votes
by (13.0k points)

Let the required zeroes be \(α\) , \(β\)

\(α + β = \frac{21}{8} = \frac{42}{16} = \frac{-b}{a}\) \(... (1)\)

\(​​​​αβ = \frac{5}{16} = \frac{c}{a}\) \(... (2)\)

From (1) and (2), 

\(b = -42\) , \(a = 16\) , \(c = 5\)

Required polynomial is

\(16x^2 - 42x + 5 \)

0 votes
by (43.8k points)

Let α & ß are zeros of quadratic polynomial.

α + ß = 21/8

⇒ -b/a = 21/8---(1)

αß = 5/16

⇒ c/a = 5/16--(2)

From (1), -b/a = 21/8 = 42/16

∴ a = 16, b = -42, c = 5

Required quadratic polynomial is

p(x) = ax2 + bx + c

= 16x2 - 42x + 5

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...