Algebra Ex 3.10-10th Std Maths-Book Back Question And Answer
Question 1.
Solve the following quadratic equations by factorization method
(i) 4x2 – 7x – 2 = 0
Answer:
4x2 – 7x – 2 = 0
4x2 – 8x + x – 2 = 0
4x(x – 2) + 1(x – 2) = 0
(x – 2) + (4x + 1) = 0
x – 2 = 0 or 4x + 1 = 0 (equate the product of factors to zero)
x = 2 or 4x = -1 ⇒ x = −14
The roots are 2; −14
(ii) 3(p2 – 6) = p(p + 5)
Answer:
3p2 – 18 = p2 + 5p
2p2 – 5p – 18 = 0
2p2 – 9p + 4p – 18 = 0
p(2p – 9) + 2(2p – 9) = 0
(2p – 9)(p + 2) = 0
2p – 9 = 0 or p + 2 =
The roots are p = 92, -2
(iii) a(a−7)−−−−−−−√ = 3 2–√
Answer:
Squaring on both sides
a(a – 7) = (32–√)2
a2 – 7a = 18
a2 – 7a – 18 = 0
(a – 9) (a + 2) = 0
a – 9 = 0 or a + 2 = 0
The roots are -2 and 9
(iv) 2–√ x2 + 7x + 52–√ = 0
Answer:
2–√ x2 + 7x + 5 2–√ = 0
2–√ x2 + 2x + 5x + 52–√ = 0
2–√ x (x + 2–√) + 5(x + 2–√) = 0
(x + 2–√) + (2–√x + 5) = 0 (equate the product of factors to zero)
x + – 2–√ = 0 or 2–√x + -5
x = −52√
The roots are – 2–√, −52√
(v) 2x2 – x + 18 = 0
Answer:
2x2 -x + 18 = 0
16x2 – 8x + 1 = (multiply by 8)
16x2 – 4x – 4x + 1
4x(4x – 1) – 1 (4x – 1) = 0
(4x- 1) (4x- 1) = 0
4x = 1, 4x = 1
x = 14, x = 14
The roots are 14 and 14
Question 2.
The number of volleyball games that must be scheduled in a league with n teams is given by G(n) = n2−n2 where each team plays with every other team exactly once. A league schedules 15 games. How many teams are in the league?
Solution:
G(n) = n2−n2
⇒ 15 = n2−n2 ⇒ 30 = n2 – n
n2 – n – 30 = 0
⇒ n2 – 6n + 5n – 30 = 0
n(n – 6) + 5 (n – 6) = 0
(n – 6)(n + 5) = 0 ⇒ n = 6, -5
As n cannot be (-ve), n = 6.
∴ There are 6 teams in the league.
