Question

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

Answer 1

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

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

Answer 2

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