Answer :
Final answer:
To find the x-intercepts of the polynomial p(x) = 45x⁴ + 66x³ - 79x² - 68x - 12, we can factor the polynomial and set each part equal to zero. Solving for x gives us the x-intercepts -1, -0.4286, 0.8571, and 0.4286.
Explanation:
To find the x-intercepts of a polynomial, we need to find the values of x where the polynomial equals zero. In this case, the polynomial is p(x) = 45x⁴ + 66x³ - 79x² - 68x - 12. To find the x-intercepts, we set p(x) equal to zero and solve for x using factoring, synthetic division, or the quadratic formula if necessary.
Let's factor the polynomial: 45x⁴ + 66x³ - 79x² - 68x - 12 = 0
Setting each part equal to zero and solving for x, we get:
x = -1
x = -0.4286
x = 0.8571
x = 0.4286
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Final answer:
To find the x-intercepts of a polynomial, we set the polynomial equal to zero and solve for x using the quadratic formula. In this case, the quadratic formula will help us find the x-intercepts of the polynomial p(x) = 45x⁴+66x³-79x²-68x-12.
Explanation:
To find the x-intercepts of a polynomial, we set the polynomial equal to zero and solve for x. For the polynomial p(x) = 45x⁴+66x³-79x²-68x-12, we need to solve the equation 45x⁴+66x³-79x²-68x-12=0. We can use factoring, synthetic division, or the quadratic formula to find the x-intercepts. In this case, it is not easy to find the rational roots or use factoring, so we can use the quadratic formula.
The quadratic formula states that for any quadratic equation of the form ax²+bx+c=0, the solutions for x can be found using the formula: x = (-b±√(b²-4ac))/(2a). In our case, a=45, b=66, and c=-12. Substituting these values into the quadratic formula will give us the x-intercepts of the polynomial.
Using the quadratic formula, we have: x = (-66±√(66²-4*45*(-12)))/(2*45). Evaluating this expression will give us the x-intercepts of the polynomial.
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