Question

solve it to prove yourself​

Answer 1

Step-by-step explanation:

$5 {x}^{2} + 3x + 7 = 0$

Let the roots of the quadratic equation are a and b. Then (a+b)= -3/5 and ab=7/5. We need to find the quadratic equation whose roots are 1/a and 1/b. So the sum of roots =

1/a+1/b =(a+b)/ab= -3/5/7/5 = -3/7 and the product of the roots = (1/a)(1/b) = 1/ab= 1/(7/5) = 5/7. The equation having 1/a and 1/b has roots is

${x}^{2} - (sum \: of \: roots)x + (product \: of \:$

$the \: roots \: = 0$

So the required equation is

${x}^{2} - ( \frac{ - 3}{7})x + \frac{5}{7} = 0 = > 7 {x}^{2} + 3x +$

$5 = 0$

Hope it helps you.