Question

find a quadratic polynomial whose zeros are alpha and beta satisfying the relation alpha + beta = 3 and alpha - beta =
$- 1$
​

Answer 1

Answer :-

Given :-

• $\sf \alpha + \beta = 3$
• $\sf \alpha - \beta = -1$

To Find :-

• Quadratic Polynomial

Solution :-

➩ $\sf \alpha + \beta = 3 \: \: \: \: \: -i$

➩ $\sf \alpha - \beta = -1 \: \: \: \: \: -ii$

Adding equation i and ii :-

➩ $\sf \alpha + \cancel{\beta} + \alpha - {\beta} = 3 - 1$

➩ $\sf 2\alpha = 2$

➩ $\sf \alpha = 1$

Substituting the value in equation i -

➩ $\sf \alpha + \beta = 3$

➩ $\sf 1 + \beta = 3$

➩ $\sf \beta = 2$

Now we have,

• $\sf \alpha = 1$
• $\sf \beta = 2$

By using factor theorem :-

If 1 is zero of a polynomial, then ( x - 1 ) is a factor of the polynomial.

Similarly, ( x - 2 ) is a factor of polynomial.

Hence,

$\sf polynomial = (x-1)(x-2)$

$\sf = x^2 - 2x - x + 2$

$\sf = x^2 - 3x + 2$

Quadratic Polynomial = x² - 3x + 2