Question

find a quadratic polynomials each with the given numbers as the sum and product of zeroes respectively
4,-3​

Answer 1

Given :-

• Sum of zeroes of a Quadratic polynomial is 4
• Product of roots in a Quadratic polynomial is -3

To find :-

• Quadratic polynomial

Solution:-

If ${\alpha,\beta}$ are the roots of Quadratic polynomial then Required Quadratic polynomial

$x {}^{2} - ( \alpha + \beta )x + \alpha \beta$

$sum \: of \: roots \: \: \: \alpha + \beta$

$\: product \: of \: roots \: = \alpha \beta$

According to Question

$\alpha + \beta = 4$

$\alpha \beta = \: - 3$

Substituting in formula

$x {}^{2} - ( \alpha + \beta )x + \alpha \beta$

$x {}^{2} - (4)x + ( - 3)$

$x {}^{2} - 4x - 3$

So, Required Quadratic polynomial is x²-4x -3