Question

Maths, Polynomial, Class - 10th

Please answer these 2 questions. For BRAINLIEST ​

Answer 1

Step-by-step explanation:

1st Question's Answer

2x² - 5x - (2k + 1) = 0

ax² + bx + c = 0

where a = 2, b = -5 and c = -(2k + 1)

Let the zeroes be y and 2y

we know that

Sum of zeroes = -b/a

y + 2y = -(-5)/2

3y = 5/2

Thus, y = 5/6

and 2y = 5/3

Now we also know that

Product of zeroes = c/a

(5/6) × (5/3) = -(2k + 1)/2

25/18 = (-2k - 1)/2

(25 × 2)/18 = -2k - 1

50/18 = -2k - 1

-2k = (50/18) + 1 = (50/18) + (18/18) = 68/18

k = -68/36 = -17/9

Thus zeroes are 5/6 and 5/3

also, k = -17/9

2nd Question's Answer

(Given as image above)

f(x) ÷ g(x)

= (2x⁴ + 4x³ - 5x² - 2x + 2) ÷ (x² + 2x - 2)

= 2x² - 1

Since the remainder is 0

Hence, g(x) is a factor of p(x)

Hope you understood it........All the best