Findthezeroesofthequadraticpolynomialandverifytherelationshipbetweenthezeroesand coeficients:12x2–4x–16
Answers
Answer:
16 is the correct answer
Explanation:
STEP
1
:
Equation at the end of step 1
((((x4)-(7•(x3)))+(22•3x2))+4x)-16
STEP
2
:
Equation at the end of step
2
:
((((x4) - 7x3) + (22•3x2)) + 4x) - 16
STEP
3
:
Polynomial Roots Calculator :
3.1 Find roots (zeroes) of : F(x) = x4-7x3+12x2+4x-16
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -16.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8 ,16
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 0.00 x+1
-2 1 -2.00 96.00
-4 1 -4.00 864.00
-8 1 -8.00 8400.00
-16 1 -16.00 97200.00
1 1 1.00 -6.00
2 1 2.00 0.00 x-2
4 1 4.00 0.00 x-4
8 1 8.00 1296.00
16 1 16.00 39984.00
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
x4-7x3+12x2+4x-16
can be divided by 3 different polynomials,including by x-4