show that 1/2 and -3/2 are the zeroes of the polynomial 4x2+4x+3 and verify the relationship between zeroes and coefficients of the polynomial
Answers
as it can be easily shown by relationship between zeroes and polynomials
here,a=4 b=4 c=3 α=1/2 β=3/2
α+β=-b/a αβ=c/a
1/2+3/2=4/4 (1/2)(3/2)=3/4
3/3=4/4 3/4=3/4
1=1
hence verified
Answer: When a polynomial is set to zero, its zeroes are the answers to the specified polynomial equation.
Step-by-step explanation:
When a polynomial is set to zero, its zeroes are the answers to the specified polynomial equation. According to the kind of polynomial, explicit formulae may be used to determine the relationship between polynomial zeroes and coefficients. An expression of the form axe + b of degree 1 is referred to as a linear polynomial. Here, "a" and "b" are constants, while "x" is a variable. The polynomial's zero is equal to -b/a, which is a constant term or x's coefficient.
Given : 1/2 and -3/2 are zeroes of polynomial 4 × 2+4x +3
To find : Verify relationship between zeroes and coefficients of the polynomial
Taking the following equation so as to show the relationship between zeroes and polynomial,
4x^2+4x+3=0
Assuming the following a=4 b=4 c=3 α=1/2 β=3/2
To find= α+β= -b/a αβ=c/a
1/2+3/2=4/4 (1/2)(3/2)=3/4
3/3=4/4 3/4=3/4
=1 =1
Since LHS= RHS,
hence verified
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