Question

if 1 and - 3 are the zeros of P (x) =x^3-ax^2-13x +bfind the value of a and b​

Answer 1

Answer:

As a cubic equation, the polynomial has three roots (although they do not have to be distinct). At present, we only know two of these roots, 1 and 3. Let us call the third root P .

We can express the equation as (x−1)(x−3)(x−P)=0

Expanding this, we get (x2−4x+3)(x−P)=0

Expanding further, we get: x3−(P+4)x2+(4P+3)x−3P=0

But we already know that the equation is x3−ax2−13x+b=0

Equating the coefficients of these two equations, we have:

x1: −13=4P+3⇒4P=−16⇒P=−4

x2: −a=−(P+4)⇒a=P+4⇒a=0

x0: b=−3P⇒b=12

So the required answer is: a=0 and b=12

Answer 2

Step-by-step explanation:

Let p(x) = x 3 – ax 2 – 13x + b

Now, p(1) = 0

(1)3 – a(1)2 –13(1) + b = 0

⇒ –a + b = 12 .....(1)

Now, , p(– 3) = 0

⇒ (– 3)3 – a (– 3)2 – 13(– 3) + b = 0

⇒ 9a – b = 12 .....(2)

Adding, equation (1) and (2),

8a = 24

⇒ a = 3

b = 12 + 3 = 15 (Using equation (1))

∴ a = 12 and b = 15