Question

Find a quadratic polynomial each with the given number as the sum and product of its

zeros respectively.

(a) ¼ , -1

(b) √2 , ⅓.​

Answer 1

Answer:

(a) sum of zero = -3/4

product of zero = -1/4

(b) sum of zero = 3√2+1/3

product of zero = √2/3

Answer 2

Answer:

$\huge \fcolorbox{black}{cyan}{♛answer♛} \\ 1. Sum \: of \: zeroes, \: S= \: \frac{1}{4} \\ </p><p>Product \: of \: zeroes, \: P = - 1 \\ </p><p>So \: required \: quadratic \: polynomial \: is \\ \: f(x) = k( {x}^{2} - Sx + P), \\ where \: k \: is \: non \: zero \: real \: number. \\ \small\bold\red{f(x) = k( {x}^{2} - \frac{1}{4}x - 1 ) } \\ 2. Sum \: of \: zeroes, \: S= \: \sqrt{2} \\ </p><p>Product \: of \: zeroes, \: P = \frac{1}{3} \\ </p><p>So \: required \: quadratic \: polynomial \: is \\ \: f(x) = k({x}^{2} - Sx + P), \\ where \: k \: is \: non \: zero \: real \: number. \\ \small\bold\red{f(x) = k( {x}^{2} - \sqrt{2} x - \frac{1}{3} ) }$