Question

if alpha and beta are zeroes of the quadratic polynomial x^2+9x+20,form a quadratic polynomial whose zeroes are ( alpha +1) and (beta +1).​

Answer 1

Answer:

${x}^{2} + 7x + 12$

Step-by-step explanation:

${x}^{2} + 9x + 20 = 0 \\ \\ \alpha + \beta = - 9 \: \: \: \: \: \: \: \alpha \beta = 20 \\ \\ s = ( \alpha + 1) + ( \beta + 1) = ( \alpha + \beta ) + 2 \\ \\ = - 9 + 2 \\ \\s = - 7 \\ \\ \\ \\ ( \alpha + 1)( \beta + 1) = \alpha \beta + ( \alpha + \beta ) + 1 \\ \\ = 20 + ( - 9) + 1 \\ \\ = 21 - 9 \\ \\ p= 12 \\ \\ polynomial \: \: \: \: \: {x}^{2} - sx + p\\ \\ {x}^{2} - ( - 7x) + 12 \\ \\ {x}^{2} + 7x + 12 .$