Answer:
Given, the polynomial is 3x² + 4x - 4.
We have to find the relation between the coefficients and zeros of the polynomial
Let 3x² + 4x - 4 = 0
On factoring,
= 3x² + 6x - 2x - 4
= 3x(x + 2) - 2(x + 2)
= (3x - 2)(x + 2)
Now, 3x - 2 = 0
3x = 2
x = 2/3
Also, x + 2 = 0
x = -2
Therefore,the zeros of the polynomial are 2/3 and -2.
We know that, if and ꞵ are the zeroes of a polynomial ax² + bx + c, then
Sum of the roots is + ꞵ = -coefficient of x/coefficient of x² = -b/a
Product of the roots is ꞵ = constant term/coefficient of x² = c/a
From the given polynomial,
coefficient of x = 4
Coefficient of x² = 3
Constant term = -4
Sum of the roots:
LHS: + ꞵ
= 2/3 - 2
= (2-6)/3
= -4/3
RHS: -coefficient of x/coefficient of x²
LHS = RHS
Product of the roots
LHS: ꞵ
= (2/3)(-2)
Step-by-step explanation:
hi
The answer is in the following image :
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Verified answer
Answer:
Given, the polynomial is 3x² + 4x - 4.
We have to find the relation between the coefficients and zeros of the polynomial
Let 3x² + 4x - 4 = 0
On factoring,
= 3x² + 6x - 2x - 4
= 3x(x + 2) - 2(x + 2)
= (3x - 2)(x + 2)
Now, 3x - 2 = 0
3x = 2
x = 2/3
Also, x + 2 = 0
x = -2
Therefore,the zeros of the polynomial are 2/3 and -2.
We know that, if and ꞵ are the zeroes of a polynomial ax² + bx + c, then
Sum of the roots is + ꞵ = -coefficient of x/coefficient of x² = -b/a
Product of the roots is ꞵ = constant term/coefficient of x² = c/a
From the given polynomial,
coefficient of x = 4
Coefficient of x² = 3
Constant term = -4
Sum of the roots:
LHS: + ꞵ
= 2/3 - 2
= (2-6)/3
= -4/3
RHS: -coefficient of x/coefficient of x²
= -4/3
LHS = RHS
Product of the roots
LHS: ꞵ
= (2/3)(-2)
= -4/3
Step-by-step explanation:
hi
The answer is in the following image :