Question

are a-b, a, a + b, find a and b.
3. If the zeroes of the polynomial
x3
- 3x²
+ x + 1​

Answer 1

Step-by-step explanation:

Question: If a-b,a and a+b are the zeros of polynomial

${x}^{3} - 3 {x}^{2} + x + 1 = 0$

then find a and b.

Concept used: If

$a {x}^{3} + b {x}^{2} + cx + d = 0$

is the cubic polynomial and

$\alpha, \: \beta \: and \: \gamma$

are the zeros of cubic polynomial,then relation between zeros and coefficient of equation is

$\alpha + \beta + \gamma = \frac{ - b}{a} \\ \\ \alpha \beta + \beta \gamma + \alpha \gamma = \frac{c}{a} \\ \\ \alpha \beta \gamma = \frac{ - d}{a}$

according to this concept ,applying the relation between zeros and coefficient of equation

$a - b + a + a + b = 3...eq1 \\ \\ 3a = 3 \\ \\ a = 1 \\ \\ a (a - b) + a(a + b) + (a - b)(a + b) = 1...eq2 \\ \\ a(a - b)(a + b) = - 1...eq3 \\ \\ put \: value \: of \: a \: in \: eq3 \\ \\ a( {a}^{2} - {b}^{2} ) = - 1 \\ \\ \because \: (x - y)(x + y) = {x}^{2} - {y}^{2} \\ \\ 1(1 - {b}^{2} ) = - 1 \\ \\ - {b}^{2} = - 2 \\ \\ {b}^{2} = 2 \\ \\ b = ± \sqrt{2}$

Value of a=1 and b = ±√2

Hope it helps you.

Answer 2

Answer:

value of a=1 and b=+ or -√2