In solving a problem, one student makes a mistake in the coefficient

• Quant Quadratic

In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was:

1. x² + 10x + 9 = 0
2. x² - 10x + 16 = 0
3. x² - 10x + 9 = 0
4. x² + 10x + 16 = 0

Answer

For a quadratic equation ax² + bx + c, the sum of roots is given by (-b/a) and product of roots is given by (c/a).

If the sum and product of roots is known, the quadratic equation can be obtained as x² -(sum)x + (product) = 0.

Since the first student makes a mistake in the coefficient of x, it means he has the correct product of roots, which is = 9.

The second student makes a mistake in the constant term, which means he has the correct sum of roots, which is = 10.

So, the equation is x² - 10x + 9 = 0.

The correct option is C.