Question

(-/5.88 Points) DETAILS LARPCALC10 2.5.035. Consider the following f(x) = -4x2 + 23x2 - 14x-5 (a) Ust the possible rational zeros of F. (Enter your answers as a comma-separated list.) X (b) Sketch the graph off so that some of the possible zeros in part (a) can be disregarded. f(x) f(x) 300 2001 00 300 200 100 -10 -5 10 - 10 -100 10 100 -200 -300 --2001 -300 f(x) 300 200 300 200 100 100 X 10 5 10 -10 -5 5 10 100 -2001 -300 -100 -2001 -300 ( Determinali real zeros of. (Enter your answers as a comma-separated list) 1,

Answer 1

All rationals zeros are also real zeros of f(x) since all rationals are real. The zeros we computed in part (a) also come in part (c). And some other zeros are also possible (other than rationals) but polynomial of three has atmost 3 zeros. Hence all rationals zeros are only possible real zeros. If you have any queries related to this question then please ask.

and it is of the Recall :- Rational Roots text If P(x) is a polynomial of degen n, and it form p(x)= an antamant axta but an to Then every rational root of pre) is of the forms *(facker glad & + do to (facloro g an a he g Given hat f(x) = -403+23x²_1485 To frid all ponsible rational zoon of eff Now from above rational root test the rooth m must be of the form : ť (fachers + 5 + 5 + 5 + + I (factars 4 It We need to check for these values and we get x=5,-1/4 all possible rooh fix) Since rooth roots of fre) +,-/ graph must cat the x-axis at ㅗ d are S. Hence 1 2 3 4 5 L 1,1%, 5. means tve x=2 check f at 2 f(3) = -448 +2344 -14X2-5=2770 f is at Hence option (1) is Srrect . (0) To determine all real geoon. Since frx) is a of degree 3. Then number of geros of fix) must be less than 3 (real genos). And from option (a) fex) has thue rational gerox and all rational, Hence all real zeron of fox) are [-1/4, 1,5 polynomial ! are real. CE