Question

If the difference of the roots of the equation $x^2 - 7x + 10 = 0$ is same as the difference of the roots of the equation $x^2 - 17x + k = 0$, then a divisor of $k$ is

• A. 14
• B. 17
• C. 6
• D. 15

Hint:

Use the formula $\text{Difference of roots} = \sqrt{a^2 - 4b}$ for a quadratic to solve problems involving root relationships.

Answer 1

The Correct Option is A

For the quadratic equation $x^2 - ax + b = 0$, the difference of roots is $\sqrt{a^2 - 4b}$.
So, for $x^2 - 7x + 10 = 0$, difference $= \sqrt{49 - 40} = \sqrt{9} = 3$.
For $x^2 - 17x + k = 0$, difference $= \sqrt{289 - 4k}$.
Equating the differences: $\sqrt{289 - 4k} = 3 \Rightarrow 289 - 4k = 9 \Rightarrow 4k = 280 \Rightarrow k = 70$.
A divisor of 70 is 14.