Question

find the values of a and b. if they are the zeroes of the polynomial
${x}^{2} + ax + b$
​

Answer 1

Solution :-

Given : a and b are the zero of the polynomial f(x) = x² + ax + b

Sum of zeros = - a

Product of zeros = b

Now,

Sum of zeros = - a = a + b

=> - a - a = b

=> - 2a = b

=> a = - b/2 ____(i)

Product of zeros = b = a × b

=> b = ab

=> b = (- b × b) /2 [from equation (i)]

=> 2b = - b²

=> b = - 2

Substituting the value of b in equation (i),

=> a = - (-2)/2 = 1

Hence,

The value of a and b are 1 and - 2 respectively.

Answer 2

Answer :

The value of a and b = 1 & - 2.

Explanation :

Given that :

a and b are the zeroes of the polynomial f(x) = x² + ax + b.

Here,

• Product of the zeroes = - a.

• Sum of the zeroes = - b.

We know that,

$\bigstar \: \boxed{ \sf{Sum \: of \: the \: zeroes=a+b=-a.}}$

Put values,

$=>\sf -a - = b. \\\\ =>\sf \: b = - 2a.\\\\=>\sf a = \dfrac{-b}{2} ........equation(1)$

We also know that,

$\bigstar \: \boxed{\sf\: Product\:of \:the\: Zeroes=b=a \times b}$

Put values,

$\sf = > b = ab \\\\ \sf => \dfrac{b = - b \times b}{2}\\\\ \sf=> 2b = - b^2 \\\\ \sf => b = - 2.$

Now,

Use the the value of b in equation 1 :

$\sf => a = \dfrac{-(-2)}{2} = 1$

Hence,

It implies that the value of :

a and b = 1 & - 2.