Question

12. If 9 and-5 are zeros of the Polynomial x*x + (a+5)x - b, then find the value of a and b.
(a) -9 and 45
(b) 9 and -35
(c) 7 and 23
(d) -7 and -23


Here, x*x means square of x

Answer 1

Answer:

Option (a) is correct.

Step-by-step explanation:

Answer is in the picture.

Answer 2

$\underline{\bigstar{\sf\ Given:-}}$

• Polynomial = x² + (a+5)x - b
• 9 and - 5 are the zeroes of the polynomial.

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$\underline{\bigstar{\sf\ To\:Find:-}}$

• Value of a and b.

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$\underline{\bigstar{\sf\ Solution:-}}$

Put x = 9 in the given polynomial:

⇒ (9)² + (a + 5) (9) - b = 0

81 + 9a + 45 - b = 0

9a - b + 126 = 0

9a - b = - 126 -----------> 1

Put x = - 5 in the given polynomial:

(-5)² + (a + 5) (-5) - b = 0

25 - 5a - 25 - b = 0

- 5a - b = 0 --------------> 2

Subtracting eq. 1 and eq. 2

9a + 5a - b + b = - 126 - 0

14 a = - 126

a = $\frac {-126}{14}$

⇒ a = - 9

Putting this value in eq. 2

⇒ - 5(-9) - b = 0

45 - b = 0

- b = - 45

⇒ b = 45

Hence , option (a) is correct.

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