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(A) For the equation $x^2-7x+10=0$,the roots are $x=2$ and $x=5$. The difference of the roots is $|5-2|=3$.For the equation $x^2-17x+k=0$,let the root

Vedclass · Accepted Answer

$14$

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(A) For the equation $x^2-7x+10=0$,the roots are $x=2$ and $x=5$. The difference of the roots is $|5-2|=3$.For the equation $x^2-17x+k=0$,let the roots be $\alpha$ and $\beta$. The difference of the roots is $|\alpha-\beta|=3$.We know that $(\alpha-\beta)^2 = (\alpha+\beta)^2 - 4\alpha\beta$.Substituting the values,we get $3^2 = (17)^2 - 4k$.$9 = 289 - 4k$.$4k = 289 - 9 = 280$.$k = 70$.The divisors of $70$ are $1, 2, 5, 7, 10, 14, 35, 70$.Comparing with the given options,$14$ is a divisor of $70$.

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

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