Question

For the roots of the equation a – bx – x² = 0; (a > 0, b > 0), which statement is true?

Options

• both roots are positive.

• both roots are negative.

• roots have opposite signs, negative root has greater magnitude.

• roots have opposite signs, positive root has greater magnitude.

Answer 1

Roots have opposite signs, negative root has greater magnitude.

Explanation:

Let roots be α and β then from the equation –x² – bx + a = 0.

We have αβ = –a < 0

Both the roots are in the opposite signs and α + β = –b < 0.

⇒ Both roots are in the opposite signs and the greater root in magnitude is negative.