Question

Find a quadratic polynomial whose zeros are a² and b² where a and b are the zeros of x²+7x+5.

Answer 1

Answer:

${x}^{2} - 39x + 25 = 0$

Step-by-step explanation:

$a + b = - 7 \\ \\ ab = 5 \\ \\ {a}^{2} + {b}^{2} = {(a + b) }^{2} - 2ab \\ = {7}^{2} - 2(5) \\ = 49 - 10 \\ = 39 \\ \\ {(ab)}^{2} = 25 \\ \\ {x}^{2} - ( {a}^{2} + {b}^{2} )x + {(ab)}^{2} = 0 \\ \\ {x}^{2} - 39x + 25 = 0$