If (x + 5) and (x – 3) are the factors of ax2 + bx + c, then values

1.	If (x + 5) and (x – 3) are the factors of ax2 + bx + c, then values of a, b and c are (1) 1, 2, 3 (2) 1, 2, 15 (3) 1, 2, -15 (4) 1, -2, 15
Answer» (3) 1, 2, -15 p(-5) = a (-5²) + b (-5) + c = 25a – 5b + c = 0 ... (1) p(3) = a (3²) + bc + 3 + c = 9 + 3b + c = 0 … (2) 25a – 5b = 9a + 3b 25a – 9a = 3b + 5b 16a = 8 b \(\frac{a}{b}=\frac{8}{16}=\frac{1}{2}\) Substitute a = 1, b = 2 in (1) 25(1) – 5 (2) = -c 25 – 10 = 15 = – c c = -15

If (x + 5) and (x – 3) are the factors of ax2 + bx + c, then values of a, b and c are (1) 1, 2, 3 (2) 1, 2, 15 (3) 1, 2, -15 (4) 1, -2, 15

Answer»

(3) 1, 2, -15

p(-5) = a (-5²) + b (-5) + c = 25a – 5b + c = 0 ... (1)

p(3) = a (3²) + bc + 3 + c = 9 + 3b + c = 0 … (2)

25a – 5b = 9a + 3b

25a – 9a = 3b + 5b

16a = 8 b

\(\frac{a}{b}=\frac{8}{16}=\frac{1}{2}\)

Substitute a = 1, b = 2 in (1)

25(1) – 5 (2) = -c

25 – 10 = 15 = – c

c = -15