Question

find a quadratic polynomial if root of the quadratic polynomial are 3 and (-1 )​

Answer 1

Let m,n are two zeroes of a

quadratic polynomial.

m = 1/2 , n = 3/2

i) m+n = 1/2+3/2 = 4/2 = 2

ii) mn = (1/2)(3/2) = 3/4

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Form of a quadratic polynomial

whose zeroes are m,n is

k[x²-(m+n)x+mn]

______________________

Here,

Required polynomial

= k[x²-2x+(3/4)]

For all real values of k it is true.

If k = 4 , then the polynomial is

4[x²-2x+(3/4)]

= 4x²-8x+3