Write a quadratic polynomial whose zeroes are 2 and ½

 Solution

Given the root of the quadratic polynomial=2 and 1/2

let ∝ =2 and β=1/2

now  ∝+β=2+1/2

=(5/2)=-b/a

=-(-5/2)=-b/a

∝β=2 x 1/2

 =2/2 =c/a

a=2 ,b= -5 ,c=2

then the Quadratic polynomail

p(x)=a(x^2 -(∝+β)x+∝β)

p(x)=2(x^2 -(-5/2)x+2/2)

p(x)=2(x^2 +5/2x+1)

p(x)=2x^2+5x+1 ans......

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write a quadratic polynomial whose zero 2 and -1/2

let ∝ =2 and β=-1/2

now  ∝+β=2-1/2=(3/2)

=-(-3/2)=-b/a

∝β=2 x \(-1/2)=-2/2

a=2 ,b= -3 ,c=-2

then the Quadratic polynomail

p(x)=a(x^2 -(∝+β)x+∝β)

p(x)=2{(x^2 -(-3/2)x+(-2/2)}

p(x)=2(x^2 +3/2x-1)

p(x)=2x^2+5x-1 ans......