Question

If 1 and -3 are the zeroes of the polynomial x 3 – ax 2 – 13 x + b , find the values of a and b

Answer 1

Answer:

a = 3 & b = 15

Step-by-step explanation:

Let α = 1 & β = -3

Here P(x) = x³ - ax² - 13x +b

Since α = 1 and β = -3 are two zeros of P(x)

Then,

P(1) = 0 and P(-3) = 0

Now,

P(1) = 0

or, (1)³ - a(1)² - 13 ×1 + b = 0

or, 1 - a ×1 - 13 + b = 0

or, 1 - a - 13 + b = 0

or, 1 - 13 = a + b

or, -12 = a - b

Therefore, a - b = -12 ............. (i)

Again,

P(-3) = 0

or, (-3)³ - a(-3)² - 13 × (-3) + b = 0

or, -27 - a ×9 + 39 + b = 0

or, -27 + 39 = 9a - b

or, 12 = 9a - b

Therefore, 9a - b = 12 ..............(ii)

Subtracting eq. (i) from (ii), we get,

8a = 24

or, a = 3

put the value of a = 3 in eq. (i) we get

3 - b = -12

or, - b = -12 - 3

or, -bb = -15

or, b = 15

Hence , a = 3 & b = 15