Given that the roots of the equation $5{{x}^{2}}-x=k+3$ differ by $3$, find the value of $k$.

Question

Given that the roots of the equation $5{{x}^{2}}-x=k+3$ differ by $3$, find the value of $k$. Find the possible values of $p$, given that the roots of the equation ${{x}^{2}}+px+3=0$ have a difference of $2$.

Accepted Answer

(i) $k=\dfrac{41}5$. (ii) $p=4$ or $-4$.

Quadratic Functions, Equations and Inequalities - Sum and Product of Roots

Quadratic Functions, Equations and Inequalities - Sum and Product of Roots

Solution:

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