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

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

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

$16x^2 - 42x + 5$

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

p(x) = ax2 + bx + c

= 16x2 - 42x + 5