Question -
Answer -
Solution:
(i) Sum of the zeroes= – 8/3
Product of the zeroes= 4/3
P(x) = x2 – (sum of the zeroes) + (product of the zeroes)
Then, P(x)= x2 – (-8x)/3 + 4/3
P(x)= 3x2 + 8x + 4
Using splitting themiddle term method,
3x2 + 8x + 4 = 0
3x2 + (6x + 2x) + 4 = 0
3x2 + 6x + 2x + 4 = 0
3x(x + 2) + 2(x + 2) =0
(x + 2)(3x + 2) = 0
⇒ x = -2, -2/3
(ii) Sum of the zeroes= 21/8
Product of the zeroes= 5/16
P(x) = x2 – (sum of the zeroes) + (product of the zeroes)
Then, P(x)= x2 – 21x/8 + 5/16
P(x)= 16x2 – 42x + 5
Using splitting themiddle term method,
16x2 – 42x + 5 = 0
16x2 – (2x + 40x) + 5 = 0
16x2 – 2x – 40x + 5 = 0
2x (8x – 1) – 5(8x –1) = 0
(8x – 1)(2x – 5) = 0
⇒ x = 1/8, 5/2
(iii) Sum of thezeroes = – 2√3
Product of the zeroes= – 9
P(x) = x2 – (sum of the zeroes) + (product of the zeroes)
Then, P(x) = x2 – (-2√3x) – 9
Using splitting themiddle term method,
x2 + 2√3x – 9 = 0
x2 + (3√3x – √3x) – 9 = 0
x(x + 3√3) – √3(x +3√3) = 0
(x – √3)(x + 3√3) = 0
⇒ x = √3,-3√3
(iv) Sum of the zeroes= -3/2√5x
Product of the zeroes= – ½
P(x) = x2 – (sum of the zeroes) + (product of the zeroes)
Then, P(x)= x2 -(-3/2√5x) – ½
P(x)= 2√5x2 + 3x – √5
Using splitting themiddle term method,
2√5x2 + 3x – √5 = 0
2√5x2 + (5x – 2x) – √5 = 0
2√5x2 – 5x + 2x – √5 = 0
√5x (2x + √5) – (2x +√5) = 0
(2x + √5)(√5x – 1) = 0
⇒ x = 1/√5, -√5/2