Question

write the factors if there zeroes (1) -2,3​

Answer 1

Step-by-step explanation:

step by step explanation

200 60%

given: zeroes of polynomial are 1/2 and

3/2

methods to solve the problem

method:

since zeroes of polynomial are given,

x = 1/2 or x = 3/2

hence we can write the above equation

as

x-1/2 = 0 or x -3/2 = 0

so we will get the polynomial we need by multiplying both the factors which are

(x-1/2)(x-3/2) = 0

multiply equation by 4 on both sides

So the required polynomial is

\boxed{ 2x^2 -4x + 3}

2.method

if alpha and beta are the roots of

quadratic equation f(x)

then the polynomial f(X) is given by

\boxed[ f(X)= K[x^2 (alpha+ beta}x+ alphax beta }

f(x) = k[ x²- sum of the zeroes + product

of the zeroes ]

sum of zeroes = 3/2+1/2 = 4/2

product of zeroes = (3/2)×(1/2) = 3/4

So the required polynomial is

\boxed[k(x^2-(4/2)x+ 3/4}