Question

Form a quadratic polynomial whose zeros are 1 and -3

Answer 1

Answer:

x^2-x-3

Step-by-step explanation:

to form a quadratic polynomial

kx[x^2-sum of zeroes*x+product of zeroes]

where k =1 so

sum of zeroes (alpha + beta) = 1

product of zeroes(alpha x beta) = -3

Answer 2

Answer:

$\huge\underline\bold\red{solution}$

$let \: \alpha = 1 \: and \: \beta = - 3$

$sum \: of \: zeroes = ( \alpha + \beta )$

$= 1 + ( - 3) = - 2$

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

$= 1 \times ( - 3) = - 3$

So,the required polynomial is:-

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

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

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