Answer:
y = x⁴- 5x² + 4
y = x(x + 3)(x - 2)
Step-by-step explanation:
1). y = x⁴- 5x² + 4
= x⁴- 4x² - x² + 4
= x²(x² - 4) - 1(x²- 4)
y = (x² - 1)(x² - 4)
y = (x - 1)(x + 1)(x - 2)(x + 2)
Therefore, zeros of this polynomial are,
x = -2, -1, 1, 2
From the given graphs, first graph has the zeros (x-intercepts) as x = -2, -1, 1, 2.
So the graph (1) represents the polynomial → y = x⁴- 5x² + 4
2). Second graph shows the x-intercepts at x = -3, 0, 2
Since, y = x(x + 3)(x - 2) is the polynomial with x intercepts at x = -3, 0, 2
Therefore, y = x(x + 3)(x - 2) represents the second graph.
