write the factors if there zeroes (1) -2,3
Answers
Step-by-step explanation:
step by step explanation
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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}