Two students solved a problem involving a quadratic equation. The first student made an error only in the constant term of the equation and determined the roots were 2 and 8. The second student made an error only in the coefficient of the linear term and determined the roots were -1 and -9. What was the quadratic equation ?

Options

A. `x^(2) - 10x + 9 = 0 `
B. ` x^(2) - 10x + 9 = 0 `
C. ` x^(2)- 10x + 16 = 0 `
D. ` x^(2) - 8x - 9 = 0 `

Answer

A

Explanation

Let correct equation is `ax^(2) + bx + c = 0 `
According to first student , equation :
`ax^(2) + bx + c _(1) = 0 ` and roots are 8 and 2
`8+ 2 = (-b)/a rArr b/a = - 10 `
Quadratic equation according to second student
`ax^(2) + b _(1) x + c = 0 " and roots " are -9 and -1`
`(-9) xx (-1) = c/a rArr c/a =9`
Putting value in original equation
`x^(2) + b/a x + c/a = 0 `
`x^(2) - 10 x + 9 = 0.`