The quartic function with only two real zeroes given as; x=5 and x=1 is; x⁴ -12x³ +46x²-60x +25
With two zeroes given for a quartic equation;
The zeroes must appear twice each such that the factors of the function are;
- (x-5), (x-5) , (x -1) and (x- 1)
The quartic function is therefore:
- (x² -10x +25) (x² -2x +1)
- (x² -10x +25) (x² -2x +1)x⁴ -2x³ +x² -10x³ +20x² -10x + 25x² -50x +25
(x² -10x +25) (x² -2x +1)x⁴ -2x³ +x² -10x³ +20x² -10x + 25x² -50x +25= x⁴ -12x³ +46x²-60x +25
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