Question

find the sum and product of zeros of polynomial x^2 + ax+ b​

Answer 1

Answer:

If a polynomial is defined as P(x)=ax^2+bx+c, then the sum of its zeroes is -b/a and the product of zeroes is c/a.

The given polynomial is

p(x)=x^2+ax+b

here, a and b are zeroes of the polynomial.

a+b=\frac{-a}{1}

a+b=-a

b=-a-a

b=-2a                 .... (1)

a\times b=\frac{b}{1}

a=\frac{b}{b}

a=1

The value of a is 1.

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Step-by-step explanation:

Answer 2

Given :

• The Given Polynomial is x² + ax + b, where a and b are the zeroes of the Given Polynomial.

To Find :

• The sum and product of the zeroes of the Polynomial.

Let us first find the value of a & b.

p(x) = ax² + bx + c

⟹ We already know that a & b are the zeroes of p(x)

So, sum of zeroes =

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

We can substitute a & b instead of $\alpha$ and $\beta$

$a + b = \frac{ - a}{1}$

$\sf{a + b = - a}$

$\sf{ b = - a - a}$

$\sf{ b = - 2a}$

Now, the product of zeroes :

$\alpha \times \beta = \frac{c}{a}$

Let us substitute the values of alpha and beta.

$a \times b = \frac{ - b}{4}$

$a = \frac{b}{b}$

$\boxed{ \sf{a = 1}}$

To find the value of b, let us substitute the value of a in b = -2a.

$b = - 2a$

$b = - 2(1)$

$\boxed{ \sf{ b = - 2}}$

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Coming to the question,

Sum of zeroes = 1 + (-2)

• Sum of zeroes = -1

Product of zeroes = 1 × -2

• Product of zeroes = -2

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